Spring, 2019
Jewett
 References (partly updated)
 ATMS 502 / CSE 566
Numerical fluid dynamics
This page is being revised as I check all the links.

For the slide (class notes) references below, slide numbers can be found near the center-top of each PPT handout slide (4 slides/page).
This list is under continuing refinement and additions.  Suggestions (for topic references) are always welcome.  Updated 1/18/2018 - links checked up through C036.

Shortcuts:  Alphabetical list of topics  /  A. Fluids  /  B. Programming+data  /  C. Numerical methods  /  Textbooks   /  Journal papers

Alphabetical listing of all topics

Topic headings (e.g. A001) refer to references in sections A (fluid flow), B (programming) or C (numerical methods) later on this page.
  • 0-gradient - see C005 (boundary conditions)
  • 1-way wave equation - see One-way wave equation; also Advection.
  • 2*dx waves - see Poorly resolved waves.
  • Accretion shock - see A006 (nonlinear transition), and Blondin, J., and A. Mezzacappa, 2006.
  • Accuracy, order of - C026
  • Accuracy, of a numerical solution - C029.  See also
  • Adaptive mesh refinement (AMR) - see Nesting.
  • Advection - A001 (fluid flow), A002 (advection), A003 (nonlinearity), A005 (1-way wave equation),
        C035 (shift condition for unit Courant number), C036 (upwind schemes - examples and problems),
        C037 (implicit viscosity), C038 (advection tests)
  • Advection-diffusion problem - see Tu et al. sec. 4.3 pp. 147-150.
  • Aliases, for commands in Linux - B017
  • Aliasing - see discussion regarding nesting (for now) - C010, Koch and McQueen paper.
  • Alternate directions [also called directional splitting or Fractional steps] - C014
  • Amplification factor: C019; C020 (von Neumann stability condition)
  • Amplitude error: C022; C019 (amplification factor), C020 (von Neumann stability condition),
        C023 (apparent amplitude "error" occurring when phase errors lead to component waves
        "adding up wrong"); C034 (modified equation - assessing dominant errors), C037 (implicit viscosity)
  • AMR - see Nesting.
  • Arakawa grids - see C012 (staggered grids)
  • Array indexing - B001 (array layout, indexing, subscripts)
  • Array layout - B001
  • Artificial viscosity (also called implicit artificial viscosity, or just numerical dissipation) - C037
  • Backward derivative - C006
  • Batch, in supercomputers - B012; see also B010 (Stampede)
  • Beta - often used in class to represent nondimensional wavenumber.
  • Big Data - B027
  • Boundary value problems - see A011 (PDE type/classification)
  • Boundary conditions - C005 (periodic), C050 (nested grid boundary conditions)
  • Boundedness - C028; also see Norms.
  • Break-even point, for grid refinement: C010, and Skamarock and Klemp 1993.
  • C programming language - B003 (Intel compiler options for debugging programs); B004 (computing information)
  • Centered derivative - C006
  • Centered space derivative - see C008 (truncation error) discussion.
  • CDGA - Continuous Dynamic Grid Adaption - see C010, and Nesting.
  • CFL (stability condition) - C043
  • Characteristics - A012
  • Characteristic equation/determinant, when solving systems of linear equations - C058, and C056 (systems of equations)
  • Cloud-resolving vs. cloud-permitting : see Resolution - C009
  • Clustering, of flagged grid points for refinement - C051, and C010 (nesting general topics)
  • CMG - Convective modeling group at the University of Illinois.
  • CMG - coarse mesh grid (i.e. the outer grid.  Acronym used in Koch and McQueen paper)
  • Color equation - A002; also see Crowley (1968) sec. 2,3, pp. 2-3.
  • Command history, in Linux - B015
  • Complex numbers - C017, C018
  • Compute nodes - B007; see also B010 (Stampede), B012 (Batch systems)
  • Computing Information - B004 (for our class on Stampede).
  • Cone problem, in advection testing - see Bott, 1982; Takacs (1985), secs. 6-10 (pp. 1055-1061);
            Crowley (1968), sec. 7 (pp. 9-11); Li 2007 (Li also available here). Also, see C038 (advection tests)
  • Conservation - C027.
  • Consistency - C013
  • Continuous Dynamic Grid Adaption (CDGA) - see C010, Nesting, and Fielder and Trapp (1993).
  • Convection-diffusion problem - see Advection-diffusion problem.
  • Convection (also called transport) - see Advection.
  • Convection (thunderstorms), and resolution - C010
  • Convergence, of a data series - see Kusse, sect. 6.7.1 pp. 150-151, sec. 7.3.1 pp. 231-232
  • Convergence, of a numerical scheme - C011; see also C053 (influence of parameterizations on convergence)
  • Convergence, of flow - opposite of divergence.  See A015 (flow types)
  • Cores, computing - B007
  • Correlation coefficient - C025
  • Courant-Fredrichs-Lewy (stability condition) - C043
  • Courant number - see C043 (CFL condition), C040 (Van Leer methods and discussion)
  • "Cross term" in multi-dimensional advection, from 2-D Taylor series - C014
  • Cylinder problem, in advection testing - see C038 (advection testing).
  • Data - see heading B, above
  • Damping - see Diffusion
  • Debugging - B002 (GNU debugger), B003 (Intel Fortran compiler options for debugging),
        B004 (compiling information for our class, on Stampede)
  • Deformation - see A015 (flow types), C038 (testing of advection schemes)
  • Dependence, domain of - see Domain of dependence
  • Derivatives - C006 (representation with finite differences); C012 (use of staggered grids);
        C026 (order of accuracy when approximating with Taylor series)
  • Difference operators - see C006 (finite differences) or C023 (finite difference operators)
  • Differential-difference equation - C061
  • Diffusion - sum of dissipation and dispersion.  See A010 (physical diffusion),
        C037 (implicit viscosity); C060 (explicit diffusion); Takacs (1985).
  • Directional splitting [Fractional steps] - C014
  • Discretization - see C008 (truncation error), C012 (staggered grids)
  • Dispersion, physical - A013
  • Dispersion, numerical (phase speed dependence on wavelength, wavenumber) - C023
  • Dissipation, added to PDE - see Durran chap. 3 (Beyond the ...) section 3.3.3 pp. 110-114.
  • Dissipation error - see Amplitude Error
  • Distortion of solution, due to phase errors - C023
  • Divergence - see A015 (flow types)
  • Domain of dependence - A014 (physical/PDE), C039 (of numerical scheme)
  • Domain of influence - see Domain of dependence
  • Donor-cell methods - see Upstream differencing
  • Eady wave - A007 (Eady wave and nonlinear transition)
  • Effective resolution - C009 (Skamarock article)
  • Efficiency, of adaptive mesh refinement - C010, and Skamarock and Klemp 1993.
  • Eigenvalue problems - C057
  • Elliptic differential equations - see A011 (PDE type/classification)
  • Explicit viscosity - see C037 (implicit viscosity)
  • Error - C024 (mean square error), C022 (amplitude error), C023 (phase error)
  • Errors - finding program code problems - B002 (GNU debugger)
  • Euler's formula (complex numbers, polar representation) - C017
  • Euler formulas - in Fourier decomposition - see C016 (Fourier series)
  • Explicit numerical methods - C002
  • Explicit diffusion - refers to adding a damping term to your PDE - C060
  • Extrema, spurious - see Dispersion [error]; monotonicity.
  • Fast Dynamic Grid Adaption Scheme - see Fiedler and Trapp 1993, and C010.
  • Feature-resolving vs. feature-permitting: see Resolution - C009
  • File - space, storage, quota, etc. - see Storage
  • File - making executable - see Shell scripting
  • Finite difference methods / approximations - C006; C023 (operator notation)
  • Finite difference operator notation / definitions - C023
  • Finite element methods - C031
  • Finite volume methods - C030
  • Fitting [rectangular] grids, as part of regridding - C051, and C010 (nesting general topics)
  • "Flagging" grid points for refinement - C051
  • Flow - A015 (2D flow types)
  • Flow speed - how implicit damping varies locally depending on the flow: C037
  • Flux form, of equations - C042; also see C040 (Van Leer methods).
  • Flux limiter - C044
  • FMG - Fine mesh grid (i.e. the inner nested grid.  Acronym used in Koch and McQueen paper)
  • Fortran - B003 (Intel compiler options for debugging), B004 (information for our class)
  • Forward derivative - C006
  • Forward time derivative - see C006; also, C007 (Taylor Series), C008 (truncation error), and C003 (time levels)
  • Fourier series - C016; C033 (applied to a square wave; Gibbs phenomenon)
  • Fractional steps [operator or directional splitting] - C014
  • Frequency, of nested grid updates - C051
  • Frequency equation, in numerical method analysis - see Differential-difference equation.
  • Fluid flow - see heading A, below
  • Fluid flow equations (A001)
  • Fluid flow, types - see Flow types.
  • Frequency - A016 (wave kinematics)
  • Front-end systems - see B007 (processors, nodes and cores), B010 (Stampede)
  • Gibbs phenomenon - C033
  • Global error - see C008 (truncation error), incl. distinction between local and global truncation error.
  • Global grid refinement - see Nesting, and papers by Skamarock and Klemp 1993, and Fiedler and Trapp 1993.
  • GNU debugger GDB - B002
  • Godunov-type schemes - see C040 (Van Leer), for now.
  • Gradients, generating sharp - to test numerical schemes.  See A015 (types of flow); See Deformation.
  • Grid refinement - see Nesting.
  • Group velocity - A018 (exact), C046 (numerical)
  • Grids - C004 (numerical stencil), C009 (resolution), C010 (refinement/nesting), C012 (staggered)
  • Grid point - vs. grid zone:  see C040 (Van Leer)
  • Grid zones - see C040 (Van Leer), for now.
  • Grid zones per second - a computational efficiency metric: B019
  • Heat diffusion or heat flow - see A010 (Diffusion)
  • High performance computing - B026
  • History, commands, on Linux - B015
  • HPC - High performance computing - B026
  • Hyperbolic differential equations - see A011 (PDE type/classification)
  • I/O redirection, in Linux - B016
  • Imaginary numbers - C018 (complex numbers)
  • Implicit numerical methods - C070
  • Implicit [artificial] viscosity (implicit damping) - C037
  • Initial value problems - see A011 (PDE type/classification)
  • Indexing - B001 (array layout, indexing, subscripts)
  • Infinite norm - see Norms
  • Influence, domain [or zone] of - see Domain of dependence
  • Input/output, redirection in Linux - B016
  • Intel Fortran - see Fortran
  • Instability - A009 (physical instability), C014 (split vs. unsplit methods, and stability),
        C015 (numerical instability),
        C019 (amplification factor and stability analysis of a numerical scheme),
        C020 (von Neumann's stability condition)
  • Kelvin-Helmholtz instability - TBA.
  • Kinematics - A016; also see A015 (Flow types)
  • Kinetic energy spectra - C009 (use for assessing resolution)
  • L2 norm - see Norms
  • Lax Equivalence Theorem - C011
  • Lax-Wendroff method - C001
  • Leapfrog method - C003 (time levels), C004 (numerical stencil), C020 (stability), C026 (accuracy),
        C054 (time differencing), C055 (computational modes)
  • Linear correlation coefficient - see Correlation coefficient
  • Linux - B015 (using/viewing command history); B016 (I/O redirection), B017 (aliases), B018 (wildcards)
  • Local error - see C008 (truncation error), incl. distinction between local and global truncation error.
  • Local functions, in a finite volume method - see C040 (Van Leer methods), for now.
  • Local grid refinement - see Nesting.
  • Login nodes - see B012 (Batch systems and running codes), B010 (Stampede)
  • Lotka-Volterra equations - C090
  • Mass store/storage systems - B013
  • Matrix norms - C021
  • Maximum norm - see Norms
  • Mean squared error - C024
  • Mesh - see Grids
  • MINMOD limiter - C044
  • Modified equation - C034.  See also Truncation error.
  • Molecule, computational - C004
  • Monotonicity, of a numerical scheme - C041
  • Multidimensional advection - see Advection
  • Numerical methods - section C
    • Explicit numerical methods - C002
    • Implicit numerical methods - C070
  • Nesting - C010, C047-C051; and C009 (Resolution); nesting errors addressed by Koch and McQueen paper
  • Nodes, computing - B007
  • Nondimensional wavenumber - wavenumber multiplied by grid spacing, e.g. k*dx.
  • Nonlinearity - A003; A006 (nonlinear transition); A007 (Eady waves), A008 (Supernovae)
  • Norms - of a vector or matrix: C021; see also Boundedness.
  • Notation - finite difference operators - C032
  • Numerical methods - see heading C, below
  • One-way nesting - outer grid run first; inner grid run later using outer grid results - C010 (Koch and McQueen paper)
  • One-way wave equation - A005; A001 and A002 (advection), A003 (nonlinearity)
  • Operator notation for finite differences - C032
  • Optimum grid nesting - C010 (Koch and McQueen paper)
  • Order, of a PDE - A004
  • Order, of accuracy of a finite difference expression - C026; also C008 (truncation error)
  • Parabolic differential equations - see A011 (PDE type/classification)
  • Parallel performance metrics/measures - B019
  • Parameterization, of physical processes - C053
  • PDEs (partial differential equations) - A004 (order), A003 (linearity), A011 (type/classification),
        A012 (characteristics), A014 (domain of dependence)
  • Pearson's (ordinary) correlation - see Correlation coefficient
  • Period - time over which a signal covers one peak to another.  Period is to time as
        wavelength is to length/dimension.  Examples of use: see C016 (Fourier series).
  • Periodic boundary conditions - C005
  • Permitting (as in cloud-permitting): see Resolution - C009
  • Phase speed - A017 (exact PDE value); see also A016 (wave kinematics)
  • Phase error - C023, C034 (modified equation - assessing dominant errors), C037 (implicit viscosity)
  • Piecewise constant, linear, parabolic methods - see C040 (Van Leer methods)
  • Polar representation, of complex numbers - C017
  • Poorly resolved waves - see C009 (Resolution)
  • Plot plots, representation of stability and phase error - see C019, C022, C023
  • Predator-Prey: see Lotka-Volterra equations - C090
  • Probabilistic CFD methods - C080
  • Processors, computer - B007
  • Propagation media, how different mesh sizes affect waves in nesting - C010, Koch and McQueen paper.
  • Programming - see heading B, above
  • Quota, disk - see Storage
  • Ranch [mass store system at TACC] - see B013 (mass storage), B010 (Stampede)
  • Regridding: placement and movement of nested grids - C051, and Skamarock dissertation
  • Resolving, as in cloud-resolving vs. cloud-permitting: see Resolution - C009
  • Richardson extrapolation, for estimating truncation error - C008; see also C010 (nesting), C051 (refinement strategy)
  • Rotation - see A015 (flow types)
  • Rotating cylinder problem - see Cylinder problem.
  • Rotating cone problem - see Cone problem.
  • Resolution - C009; and C010 (Nesting)
  • Resolving (as in cloud-resolving): see Resolution - C009
  • Shell scripting - B014; see also B017 (aliases), B018 (wildcards)
  • Shift condition - C035.
  • Slopes - computed for piecewise linear method - C040 (Van Leer methods).
  • Slope limiters - C044
  • Smolarkiewcz - deformation test (see Deformation); advection findings discussed in C014.
  • Spectra, kinetic energy - C009.
  • Speedup - B019
  • Splitting, directional [or operator, also called Fractional Steps] - C014
  • Sponge boundary conditions - see Tendency Blending.
  • Spurious noise/waves, due to nesting - C010
  • Squall line, sensitivity to resolution - C010.
  • Square wave, also called top hat function - see C016 (Fourier series) for examples.
  • Square wave - see C016 (Fourier series), C033 (Gibbs phenomenon)
  • Scratch [disk space] - see Storage
  • Stability - is boring.  See Instability.
  • Staggered grids - C012
  • Stampede, TACC supercomputer resource - B010
  • Stencil, numerical - C004
  • Stochastic methods in CFD - see C080
  • Storage - see B011 (high-performance file systems), B013 (mass storage systems), B010 (Stampede supercomputer)
  • Subscripting - B001 (array layout, indexing, subscripts)
  • Supernovae - A008 (Supernovae and nonlinear transition)
  • Taylor Series - C007; and C008 (truncation error); C001 (deriving Lax-Wendroff from Taylor Series)
  • Tendency bleeding - typo error on my part.  See Tendency Blending.
  • Tendency blending, also called sponge boundary - see nesting discussion, C010 (Koch and McQueen paper)
  • Time-dependent boundary conditions, in nesting - C050
  • Time for features to move one grid length dx - see C043 (CFL, and Courant number)
  • Time filtering, for methods with computational modes - C055
  • Time levels, of numerical methods - C003
  • Translation - see A015 (flow types), IMDB (lost in)
  • Transport - see Advection.
  • Tremback, Craig J. - see C036 (upstream advection schemes)
  • Truncation error - C008; and C007 (Taylor Series), C034 (Modified equation)
  • Turbulence - C010 (resolution changes needed for development)
  • Uncertainty analysis in CFD - see C080
  • Unsplit operators/advection - see C014
  • Update frequency [of movement of grid], in nesting - C051
  • Upstream Non-Oscillatory (UNO) advection schemes - see C036 (upwind schemes), Li 2007(also available here).
  • Upwind- (or Upstream-) advection schemes - C036; also see C037 (implicit viscosity/dissipation); and
        also see C034 (modified equation for upstream and other methods)
  • Van Leer methods - C040
  • Vector norms - C021
  • Viscosity, implicit - C037
  • Visualization - see heading B, below
  • von Neumann's method for stability analysis - C020
  • Vorticity - see A015 (flow types), C038 (alternating pattern to produce deformation)
  • Wave kinematics - see Kinematics.
  • Wavenumber - number of wavelengths in a domain.  For more information,
        see A016 (wave kinematics), and discussion accompanying polar plots: C019, C022, C023
  • Wavenumber-dependent phase errors - when a numerical scheme erroneously (for the 1-way wave
        wave equation with constant flow) moves some waves faster than others; see C023 (dispersion)
  • Wavelength - dimensional (e.g. meters) length from e.g. one wave peak to another.  For more
        information, see discussion accompanying polar plots: C019, C022, C023
  • Weak solution - see C011 (convergence)
  • WORK - disk space:  see Storage
  • XSEDE - Extreme Science and Engineering Discovery Environment - B005 and xsede.org
  • Zero-gradient - see C005 (boundary conditions)
  • Zhang (1986), paper on optimum grid nesting - C010 (Koch and McQueen paper)
  • Zone of dependence - see Domain of dependence

A. Fluid dynamics and kinematics

  • A001 - Fluid flow equations.
    •   See Tu et al., Chap. 3 "Governing equations for CFD - fundamentals"
    •   See Durbin, sec. 1.3 (Navier-Stokes Equations), pp. 5-10.
    •   See Holton, Chap. 1 (Introduction) pp. 1-24.
    •   See Cushman-Roisin and Beckers, Chap. 3 (Equation of Fluid Motion), pp. 77-83.
    •   Short form: see Braithwaite - see Brian , chaps. 1 (Introduction) and 2 (Ideal fluids: basic concepts).
    •   See Kreiss and Lorenz, Chap. 1 sec. 1.2 (Derivation of the Navier-Stokes Equations) pp. 9-18.
  • A002 - Advection.
  • A003 - Nonlinearity.
    •   PDEs: Kusse, chap. 10 sec. 10.1.3 (Linear vs. nonlinear equations), p. 340.
    •   And shallow water waves: Kundu sec. 7.6 (Nonlinear waves in shallow and deep water), pp. 279-286 esp. Fig. 7.19.
    •   And K-H instability:  see Braithwaite (see Brian) sec. 4.3, pp. 28-34, esp. Fig. 4.7 and p. 33.
    •   And error growth and data assimilation:  see Cushman-Roisin and Beckers, Chap. 22, pp. 726-730.
    •   And wave interaction:  see Cushman-Roisin and Beckers, Chap. 16, pp. 539-542.
  • A004 - PDE order.
    •   See Kusse, chap. 10 sec. 10.1.4, p. 341.
    •   See Durran, pp. 2-3.
    •   More general:  Arfken, chapter 9.
  • A005 - 1-way wave equation
  • A006 - Nonlinear transition.
    •   And K-H instability:  see Braithwaite (see Brian) Fig. 4.7 and discussion (pp. 32-33).
    •   And Benard convection:  see Kundu, sec. 11.4, p. 491, last paragraph.
    •   And local grid refinement as instability evolves and turbulence develops:  Tu et al., Chap. 7, pp. 322-323.
    •   In simulations of 'core-collapse supernovae' - see Blondin, J., and A. Mezzacappa, 2006.
  • A007 - Eady wave - nonlinear transition.
    •   See Holton, sec. 8.4.3 (The Eady stability problem), pp. 257-260.
    •   See Hyun and Fowlis, 1979:  The wave structure of the Eady model of baroclinic instability. Library link; PDF.
  • A008 - Supernova - nonlinear transition.
  • A009 - Instability (physical).
    •   General concepts:  try Wikipedia.
    •   And K-H instability:  see Braithwaite (see Brian) sec. 4.3, pp. 28-34, esp. Fig. 4.7 and p. 33.
    •   Chapters:  see Kundu (Fluid Mechanics, chapters 11 and 12);
             Lindzen (Dynamics in Atmospheric Physics, chapter 13);
                   Braithwaite (see Brian) (An Introduction to Hydrodynamics, chapter 4)
    •   Books: Charru (Hydrodynamic Instabilities),
                   Cushman-Roisin and Beckers (Intro. to Geophysical Fluid Dynamics);
             Yaglom (Hydrodynamic Instability and Transition to Turbulence).
  • A010 - Diffusion (physical).
    •   See Arfken sec. 9.7 (Heat-Flow, or Diffusion PDE) pp. 437-444.
    •   See Durran p. 128 (molecular diffusivity)
    •   See Wesseling pp. 57 (parabolic equations)
    •   See Kundu p. 311 (diffusion of vorticity and of heat).
    •   See Kusse sec. 10.7.4, pp. 391-398 - solution with Greens function approach.
    •   In general, references on 'heat diffusion' or 'parabolic PDEs' may be useful.
    •   See also C060 (explicit diffusion, in a PDE being solved)
    •   Advection+diffusion:  see, e.g., Cushman-Roisin and Beckers pp. 163-167 and Wesseling pp. 33-34.
  • A011 - PDE type (elliptic, parabolic, hyperbolic, initial/boundary value problems).
    •   Common PDEs - Arfken Chap. 9 (PDEs), Sec. 9.1 (Introduction - Examples of PDEs).
    •   See Arfken Chap. 9 (PDEs), sec. 9.3 (Second Order Equations - Classes of PDEs), pp. 409-411.
    •   See Wesseling Chap. 2, sec. 2.2 (Classification of PDEs) pp. 54-60.
    •   See Durran, pp. 4-11 (considers first and second-order equations)
    •   See Bronson and Costa, Chap. 1 (Basic Concepts) sec. 1.4, and:
              for initial value problems, chaps. 1, 4, 13 and 26; for second-order boundary-value problems, chap. 32.
    •   See Holton, sec. 10.8 p. 360, for distinctions between initial- and boundary-value problems in weather models.
    •   See Kreiss and Lorenz Chap. 7 (Initial-Boundary Value Problems in One Space Dimension)
    •   For parabolic problems, see also A010 (Diffusion), above.
  • A012 - PDE characteristics.
    •   See also A014 (physical PDE domain of dependence), C039 (domain of dependence of numerical scheme)
    •   See Arfken Chap. 9 (PDEs) sec. 9.2 (First-order equations - Characteristics), pp. 404-406.
    •   See Cushman-Roisin and Beckers sec. 6.4, pp. 172-173: characteristics for 1-way wave equation.
    •   See Durran Chap. 1 (PDEs), pp. 4, 5, and 9.
    •   See Holton, sec. 13.3.3, p. 457 (characteristics of 1-way wave equation)
    •   See Wesseling, Chap. 2 (PDEs), pp. 70-71, 75-78; and Chap 8 (shallow water equations) pp. 310-311 & Fig. 8.1.
    •   See Anderson, pp. 20-24.
  • A013 - Dispersion (physical).
    •   See Durbin, p. 321, "when speed depends on wavelength..."
  • A014 - Domain of dependence and Domain of influence (physical, for a PDE). 
    •   See Wesseling, Chap 8 (shallow water equations) pp. 310-311 & Fig. 8.1.
  • A015 - Flow types (2D).
    •   See Durst, Chapter 4 (Basics of fluid kinematics)
    •   See Pozrikidis, Chapter 2 (More on kinematics)
  • A016 - Wave kinematics.
  • A017 - Phase speed (exact).
  • A018 - Group velocity (exact).
    •   See Cushman-Roisin and Beckers, Appendix B (Wave kinematics), sec. B.3, pp. 778-780.
    •   See Holton, sec. 7.2.2, pp. 186-188.
    •   See Durbin, Chap. 8, sec. 8.3.1 (Group velocity and its connection to surface excrescence), pp. 323-326.
    •   See discussion on phase vs. group velocity, and this web app.
  • A019 - Density currents. 
  • A020 - Inviscid flow
    •   see Braithwaite (see Brian) p. 47-48 (Frictionless flow past a sphere), p. 46 (Viscosity and flow at high Re number), p. 49
    •   see Yaglom, sec. 1.1 (Principal equations of fluid mechanics), 1.2 (Examples of exact/approximate solutions), p. 15.
    •   see Holton 4th edition sec. 1.4.3 (Viscous force), pp. 8-10.
    •   see Kundu, sec. 1.5 (Molecular transport phenomena), pp. 7-8.
    •   see Durbin, sec. 1.2 (Viscosity) pp. 2-5.
  • A021 - Euler equations (approximation)
    •   see Kundu, sec. 4.6 (Navier-Stokes momentum eqn) p. 115 bottom,
                           sec. 4.9 (special forms of equations) p. 128 eqn. 4.66.
    •   see Durran, sec. 1.2.1 (Hyperbolic equations), pp. 16-17; linearized version p. 18 equations (1.41-1.44).
  • A022 - CFD equations: Momentum
    •   see Durbin, sec. 1.3 (Navier-Stokes equations), pp. 6-9.
    •   see Tu et al., sec. 3.3 (The momentum equation), pp. 70-84.
    •   see Holton 4th ed. sec. 3.1.1 (Horizontal momentum equation), pp. 57-58.
    •   see Cushman-Roisin, sec. 3.2 (momentum budget) pp. 78-79
  • A023 - CFD equations: Pressure (diagnostic, prognostic, and the Exner function)
    •   Diagnostic pressure:
      • see Durran, sec. 8.1 (Projection method) p. 395 eq. 8.4, sec. 8.1.1 p. 396 eqn. 8.9, sec. 8.1.2 pp. 397-398.
    •   Prognostic pressure, quasi-compressible system:
    •   Exner function:
  • A024 - CFD equations: Continuity
    •   see Tu et al. sec. 3.2 (The continuity equation) pp. 61-70.
    •   see Kundu sec. 4.2 (Conservation of mass) pp. 96-99.
    •   see Holton 4th ed. sec. 2.5 (The continuity equation) pp. 42-46.
    •   see Cushman-Roisin sec. 3.1 (Mass budget) p. 77.
  • A025-28: Reserved
  • A029 - Compressibility
    •   see Cushman-Roisin sec. 11.3 (A note on atmospheric stratification) pp. 349-350.
    •   see Tu et al. sec. 8.2.2 (Compressible flows) pp. 352-359.
    •   see Yaglom, sec. 1.1 (Principal equations), p. 2 (bottom),
           and pp. 4-5 (closing equation set for thermally inhomogeneous fluids)
    •   see Durbin, chapter 7 (Compressible flow), pp. 264 fwd;
          including sec. 7.5 (Computation of compressible flows), pp. 300-303.
  • A030 - Incompressible approximation
    •   see Tu et al. sec. 8.2.1 (Incompressible flows) pp. 349-352.
    •   see Kundu sec. 4.5 (Constitutive equation for a Newtonian fluid) pp. 113-114.
  • A031 - Boussinesq approximation
    •   see Kundu sec. 4.9 (Special forms of the equations) pp. 135-137.
    •   see Durran sec. 1.2.2 (Filtered equations) pp. 21 and 24; also p. 395 eqn. 8.1-8.4.
    •   see Holton 4th ed. sec. 5.1.1 (The Boussinesq approximation) p. 117 and p. 197.
    •   see excellent online reference by David Randall, Colorado State University.
  • A032 - Anelastic approximation
  • A033 - Quasi-compressible approximation
  • A034 - Hydrostatic approximation
    •   see Durran sec. 8.5 (The Quasi-hydrostatic approximation) pp. 431-433 and eqn. 8.92.
    •   see Holton 4th ed. sec. 1.6.1 (The hydrostatic equation) pp. 20-21,
          and sec. 2.4.3 (The hydrostatic approximation) pp. 41-42.
    •  see Cushman-Roisin sec. 4.3 (Scales of motion), pp. 105-106, eqn. 4.19;
          sec. 11.3 (A note on atmospheric stratification) p. 351
  • A035 - Geostrophic approximation
    •   see Holton 4th ed. sec. 2.4.1 (Geostrophic approximation and geostrophic wind) p. 40,
          and sec. 2.4.2 (Approximate prognostic equations; the Rossby Number) p. 41,
          and sec. 6.2 (Quasi-geostrophic approximation) p. 146 fwd.
  • A036 - Frontogenesis (formation of a front, a localized region of intensified thermal contrast)
  • A037-39: Reserved
  • A040 - Sound waves
    •   see Holton 4th ed. sec. 7.3.1 (Acoustic or sound waves) pp. 189-192.
    •   see Durran sec. 1.2.1 (Hyperbolic equations): equations and sound speed p 18, dispersion relation p. 20,
          sec. 1.2.2 p. 20-21 (Filtered equations - eliminating sound waves),
          sec. 8.0 pp. 393-394 (Physically insignificant fast waves).
    •   see Durbin, sec. 7.2 (Mach waves), pp. 271-276.
  • A041 - Nonlinear instability (physical)
    •   see Durran sec. 4.5 (Burger's equation), pp. 188-193

B. Programming, data, and visualization

C. Numerical methods

  • C001 - Lax-Wendroff method.
  • C002 - Explicit numerical methods.
    •   See Durbin, pp. 86-87.
    •   See Tu et al., Chap. 4 "The basics," sec. 4.3.3 pp. 148-150.
    •   See Holton, sec. 13.3.2, pp. 454-455.
    •   See Wikipedia.
  • C003 - Time levels.
    •   See e.g. Tu et al. Chap. 4 "The basics," sec. 4.3.3 pp. 149-150 including Fig. 4.8 and 4.9.
  • C004 - Numerical stencil / Numerical or computational molecule.
    •   See Tu et al, Chap. 4 "The basics" sec. 4.2 pp. 126-127, including Fig. 4.2, and example 4.1 on pp. 132-133.
    •   See Wesseling, sec. pp. 81, 89; chap. 11 p. 467 onward.
    •   For staggered grids in particular, see C012.
  • C005 - Periodic boundary conditions.
  • C006 - Finite difference approximations.
    •   Highly recommended:  Tu et al., chap. 4 "The Basics," sec. 4.2.1 "Finite-difference method", pp. 125-130.
    •   Also very clear:  lecture notes from MSC321, Univ. Miami (Mohamed Iskandarani)
    •   See Kundu, chapter 10, section 10.2, "Finite-difference method."
    •   See Durran, sec. 1.3.1 pp. 26-28, "Approximating calculus with algebra",
            and sec. 2.1.1, p. 37, "truncation error"
    •   See Holton, secs. 13.3.1-13.3.2, pp. 452-455.
    •   See Wesseling p. 84.
    •   Ferziger, sec. 2.6.1, pp. 35-36.
    •   For finite difference operator notation, see C032.
    •   Formulae for approximations to derivatives: page from David Eberly
    •   For a short description and list of some low-order formulae: page from Jan Hesthaven
  • C007 - Taylor series.
  • C008 - Truncation error.
    •   See Tu et al., Chap. 4 "The basics," sec. 4.2.1 pp. 127-130.
    •   See Durran, pp. 36-38, 92.des
    •   See Holton sec. 13.3.6, pp. 460-461.
    •   See Kundu, chapter 10, pp. 426-428.
    •   Local vs. global truncation error -
            See       Tu et al. 2007 sec. 5.5.1.1 pp. 196-199; also Wesseling, pp. 166-167.
    •   Also see Order of Accuracy (C026)
  • C009 - Resolution, and feature-resolving vs. permitting
    •   In atmospheric sciences - research has suggested that physical features must be at least 4-6 grid points
        across (newer work suggests 5-7*dx for WRF model) in order to be faithfully represented. 
    •   See Kundu Chap. 10 sec. 10.1 "Discretization and its accuracy"
    •   Ross' work (1966) is quoted in the Navy Forecasters' Handbook p. 9-1
    •   See also C008 (truncation error), though they don't examine errors in the same way as Skamarock.
    •   Feature resolving vs. permitting: see Craig and Dornbrack 2008, and perhaps Bryan et al. 2003
  • C010 - Adaptive grid refinement; Nesting. 
    •   Wikipedia.
    •   See Durbin, sec. 2.1.5 (Mesh quality), pp. 74-78.
    •   See Wesseling, sec. 4.3 (Numerical experiments on locally refined one-dimensional grid), pp. 120-122.
    •   In response to development of instability and turbulence:  Tu et al., sec. 7.4, pp. 322-323.
    •   Textbook discussing application: Numerical Methods in Astrophysics (Eng. library; google).
    •   Grid nesting in the GFDL atmospheric dynamical core (GFDL link).
    •   Atmospheric sciences specific references -
      • Bryan and Morrison (2012), Sensitivity of a simulation squall line to horizontal resolution ... : Link, PDF.
      • Bryan et al. (2003), Resolution requirements for the simulation of deep moist convection: Link, PDF.
      • Fiedler and Trapp (1993) - Continuous Dynamic Grid Adaption (CDGA): Link, PDF
      • Harris and Durran (2010) - An idealized comparison of one-way and two-way grid nesting: PDF
      • Koch and McQueen - see Brian
      • Weisman et al. (1997), The resolution dependence of explicitly modeled convective systems: Link, PDF.
      • Skamarock et al. (1993), Adaptive grid refinement for 2-D and 3-D nonhydrostatic atmospheric flow: Link, PDF.
      • Skamarock - Dissertation, Stanford: Download link
      • Warner and Hsu (2000), The impact of coarse-grid parameterized convection on fine-grid resolved convection: Link
      • Zhang et al. (1986) - A two-way interactive nesting procedure with variable terrain resolution: Link
    •   Good introductory document on aliasing, 11 pages, author unknown - from Carnegie Mellon
  • C011 - Convergence; Lax equivalence theorem.
    •   See Durran, pp. 38-40, 92-94; to a weak solution, 213.
    •   See Kundu, chapter 10, pp. 426 and 428.
    •   Ferziger, sec. 2.5.2, p. 32.
    •   Tu et al., sec. 5.4, pp. 188-195.
  • C012 - Staggered grids.
    •   See Ferziger, pp. 164-167, sec. 7.2, and pp. 225-226, section 8.4 - "Choice of Variable Arrangement"
    •   See Durran, pp. 153-157 : temporal and spatial staggering, pp. 167-169 : systems of equations
    •   See Wesseling, p. 81, 89, sec. 6.4 pp. 240-244, and chapter 11 pp. 467 onward
    •   See Kundu, chapter 10 pp. 443-445 including their Fig. 10.4
    •   See Griebel, pp. 26-28 : treatment of the spatial derivatives
    •   See "Why should we use staggered grid" link; see also "Arakawa grids" link;
  • C013 - Consistency.
  • C014 - Directional (or Operator) splitting; also called Fractional Steps or Alternate Directions. 
                This includes "cross term" discussed by Smolarkiewicz.
    •   See Durran, pp. 169-176.
    •   See Guinot, chapter 7 - sec. 7.2 (Alternate Directions), pp. 304-309.
    •   See Wesseling, p. 259 : PISO (pressure implicit with splitting of operators, not really directional) method.
  • C015 - Instability (numerical).
    •   See Durbin sec. 6.5 pp. 254-262: Instability theory.
    •   See Kundu chapter 10 pp. 426-428.
    •   See Durran, sec. 3.2, pp. 92-100 (Stability and convergence)
    •   See Ferziger, sec. 2.5.2 (Stability), p. 32.
  • C016 - Fourier Series.
  • C017 - Euler's formula.
    •   See Wikipedia link.
    •   See Arfken, sec. 1.8 pp. 56-57, "Complex numbers - Polar Representation."
    •   See Kusse, sec. 6.1.3 p. 136-137, "Exponential function and polar representation."
  • C018 - Complex numbers.
    •   See Kusse, sec. 6.1 pp. 135-137, "A complex number refresher."
    •   See Arfken, sec. 1.8 pp. 53-55, "Complex numbers and functions - Basic properties."
    • .... //// References checked up to this point, March 2017
  • C019 - Amplification factor.
    •   See Durran, pp. 40, 44, and 96.  For systems of equations, sec. 4.1.1 pp. 148-150.
    •   See Tu et al., sec. 5.3, pp. 182-188.
    •   See also C022 - amplitude error.
  • C020 - von Neumann stability condition.
  • C021 - vector, matrix norms.
    •   See Durran, sec. 3.2, pp. 92-94 (vector norms); sec. 4.1.1.1, pp. 148-149 (matrix norms).
    •   See Wesseling, p. 88 and 169-172 (L2 and maximum norms)
  • C022 - Amplitude error (dissipation).
    •   See Durran pp. 43-44, and 110.
    •   See Durbin pp. 84-86.
  • C023 - Phase error (dispersion is phase speed dependence on wavenumber, wavelength).
    •   See Durran pp. 43-44 and 109-110.
    •   See Durbin pp. 84-86.
    •   See Wilks p. 367.
    •   See Holton, Chap. 13 (numerical modeling and prediction), sec. 13.3, p. 461.
    •   For dispersion associated with physical phenomena, see A013.
    •   See also C034 (Modified equation) for references on dissipation vs. dispersion.
  • C024 - Mean square (total) error.
    •   See Wilks, sec. 8.3.2 pp. 325-327; also sec. 8.6.3 pp. 359-364.
  • C025 - Correlation coefficient.
  • C026 - Order of accuracy (in approximations to derivatives)..
    •   See Durran, p. 37.
    •   See Tu et al., Chap. 4 "The basics," sec. 4.2.1 pp. 127-130.
    •   See Durbin p. 77 (in context of mesh grids and Taylor series), and p. 83
    •   See Kundu, Chap. 10 sec. 10.2 (discretization and its accuracy)
    •   See Tremback et al. (1987)
  • C027 - Conservation.
  • C028 - Boundedness.
  • C029 - Accuracy (of a numerical solution)
    •   See also C008 (truncation error), C009 (resolution), C022 (amplitude error),
                  C023 (phase error), C026 (order of accuracy)
    •   Ferziger, sec. 2.5.7, pp. 34-35.
    •   Tu et al., sec. 5.5, pp. 195-205.
  • C030 - Finite volume methods.
    •   Tu et al., sec. 4.2.2 pp. 130-135, sec. 4.3.2 pp. 138-140.
    •   Durbin, sec. 2.2.1 (Discrete equations), pp. 79-80.
    •   Ferziger, sec. 2.6.2, p. 36.
    •   See Durran Chapter 5.
    •   Comparison with finite difference methods:  Tu et al., sec. 4.3.3 pp. 140-150.
    •   See Cushman-Roisin and Beckers sec. 3.9 ("Finite volume discretization"), pp. 88-92.
  • C031 - Finite element methods.
  • C032 - Operator notation for finite differences.
  • C033 - Gibbs phenomenon.
    •   See Arfken, Chapter 19, sec. 19.3 (pp. 957-961).
    •   Fourier series and the square wave: online link.
    •   Windowing methods to reduce Gibbs effect:  online link.
  • C034 - Modified equation.
    •   See also C008 (truncation error), C035 (shift condition)
    •   Durran, sec. 3.3.2, pp. 109-110.
  • C035 - Shift condition. (needs reference!)
  • C036 - Upwind/upstream advection schemes - methods and problems.
    •   Examples of higher-order schemes:  Tremback et al. 1987.
    •   Upwind and centered differencing - Durbin, sec. 2.2.2, pp. 82-86.
    •   For ocean models:  Li 2007 (also available here).
    •   Higher-order: Tu et al. Appendix B, pp. 401-402.
      •
  • C037 - Implicit viscosity [dissipation].
    •   See also C036 (upwind advection schemes)
    •   Durran sec. 3.3.2, p. 110 (top of page) - this is numerical dissipation.
  • C038 - CFL - mistakenly numbered on 2013 slides.  CFL is now listed under C043.
  • C038 - Advection tests
    •   Deformational flow (to test advection schemes)
  • C039 - Domain of dependence, domain of influence (numerical).
    •   See Holton, sec. 13.3.2, p. 455, Fig. 13.1 (domain of dependence); also p. 457 (domain of influence).
    •   See Durran, sec. 3.2.3, pp. 98-100, including Fig. 3.1 on p. 99.
    •   See Cushman-Roisin and Beckers sec. 6.4, pp. 172-177, including:
      • numerical domain of dependence for Leapfrog (see Fig. 6.5 on p. 175)
      • numerical domain of dependence for Upstream (see Fig. 6.7 on p. 177)
  • C040 - van Leer methods.
    •   Concepts:  grid zones, local functions:  Flux form: C042.
    •   Piecewise linear routine used in class -
    •   Piecewise linear slope limiter - see C044.
  • C041 - Monotonicity.
    •   See Cushman-Roisin and Beckers, sec. 61, bottom of page 166 to top of p. 167.
    •   See Durran, sec. 5.2.2, p. 215 ("monotonicity preserving" methods).
    •   See Wesseling, sec. 9.2, p. 340, "monotonicity preservation".
    •   See C044 (MINMOD monotonic slope limiter for piecewise linear method)
  • C042 - Flux form of equations.
  • C043 - CFL (Courant-Fredrichs-Lewy) condition.
    •   See Holton, sec. 13.3.3, p. 457.
    •   See Durran, sec. 3.2.3, pp. 98-100.  Includes Courant number (p. 100).
    •   See also A014 (physical/PDE domain of dependence), C039 (domain of dependence for numerical scheme)
  • C044 - (slope or flux) limiters.
    •   See Durran, sec.5.5.2 ("Possible flux limiters"), pp. 230-234.
    •   See Wikipedia - yes, they cover that, too.  Here is a PDF version; look for "Generalised minmod limiter" for van Leer.
    •   See Cushman-Roisin and Beckers, chap. 6, pp. 182-183 - purpose of a "limiter" and also
             sec. 15.7 ("Nonlinear advection schemes") pp. 507-512 and Fig. 15.16.
    •   See this lecture ("Chapter 4"), sec. 4.4 and 4.4.2, in fluid dynamics lectures by C. P. Dullemond.
    •   See Durbin, sec. 7.5 (Computation of compressible flows), pp. 300-302 - esp. discussion of shocks at top of p. 301.
  • C045 - Phase speed (numerical).
    •   See Durran, sec. 3.3.1 (Differential-difference equations and wave dispersion), pp. 101-104;
          discusses stationary (phase speed = 0) 2*dx waves (see Fig. 3.3, p. 104)
  • C046 - Group velocity and group velocity error (numerical).
    •   See Durran, sec. 3.3.1 (Differential-difference equations and wave dispersion), pp. 101-105;
          discusses negative group velocity for 2*dx waves (see Fig. 3.5, p. 105)
    •   See University of Virginia web application (requires Java)
  • C047 - Nesting:  General comments; Irregular grids; and global grid refinement.
    •   See Skamarock et al. (1993), sec. 1b (Other adaptive approaches), pp. 789-790 on added, divided and moving grid cells.
    •   See Tu et al. sec. 8.2.2.2 (Adaptive meshing), pp. 357-359 and Fig. 8.3 on p. 359.
  • C048 - Nesting:  time integration.
  • C049 - Nesting:  Coding and tasks (sequence of operations).
  • C050 - Nesting:  Boundary conditions.
  • C051 - Nesting:  Grid refinement strategy, placement and movement. 
    •   See Skamarock's Ph.D dissertation from Stanford - link here.
    •   Also, see C010 - adaptive grid/mesh refinement
  • C052 - Advection techniques.
    •   Very general heading.  This will be filled in later.  For now:  TBA
  • C053 - Parameterization of physical (esp. subgrid) processes.
    •   See Cushman-Roisin and Beckers, Chap. 1 p. 28 (first mention of parameterization),
          Chap. 4 sec. 4.2 p. 101 (subgrid-scale motions), Chap. 11 sec. 11.4 p. 354 (convective parameterization),
          Chap. 18 sec. 18.4 p. 616 (parameterizations vs. directly simulating turbulence),
          Chap. 19 sec. 19.6 p. 643 (cloud parameterization),
          Chap. 20 sec. 20.6 p. 685 (resolution and subgrid parameterization)
    •   See Holton, sec. 11.3 p. 393 (parameterizing cumulus heating), sec. 13.6.3, pp. 474-475 (overview of problem)
  • C054 - Time differencing.  Leapfrog:
    •   see Durran, Chap. 2 (Ordinary differential equations); specifically sec. 2.2.3 (Single-stage, single-step schemes) p. 44,
          sec. 2.3 (Runge-Kutta/Multistage methods) p. 49, sec. 2.4 (Multistep methods) p. 58 -
          for Leapfrog, see sec. 2.4.1 (Explicit 2-step schemes) p. 59,
              sec. 2.4.2 (controlling the leapfrog computational mode) p. 62
  • C055 - Computational modes.
    •   See Cushman-Roisin and Beckers, Chap. 6, sec. 6.4, p. 174.
    •   See Durran, sec. 2.4.1 ("Explicit two-step schemes"), p. 59, and
                            sec. 2.4.2 ("Controlling the Leapfrog computational mode"), pp. 62-67.
  • C056 - Systems of linear equations.
    •   See Arfken, Chapter 2, sec. 2.1, p. 83.
  • C057 - Eigenvalue problems.
  • C058 - Characteristic equation/polynomial in a homogeneous linear equation system.
    •   See Arfken, Chapter 6, sec. 6.2, example ending on pp. 302-303.
  • C059 - reserved for later.
  • C060 - Diffusion (explicit, added to PDE).
    •   See Durran, sec. 3.3.3 (Artificial dissipation), pp. 110-114, and discussion regarding Fig. 3.8 on p. 112.
  • C061 - Differential-difference equation (isolating role of just time or space differencing).
    •   See Durran, sec. 3.3.1 (Differential-difference equations and wave dispersion), pp. 101-108.
    •   See Durbin, sec. 2.2.2 (Centered and upwind differencing), p. 85 - what Durbin calls the semidiscrete equation.
  • C062-64: Reserved
  • C065 - Quasi-compressible approximation (application in CFD)
    • For now, see A033.
  • C070 - Implicit numerical methods.
    •   See Durbin, pp. 86-88.
    •   See Tu et al., Chap. 4 "The basics," sec. 4.3.3 pp. 149-150; and: Chap. 5 pp. 192 and 206, Chap. 8 pp. 368-369.
      • also: Solving algebraic equations, sec. 404, pp. 150-159.
    •   See Holton, Chap. 13 (numerical modeling and prediction) sec. 13.3.4, pp. 458-459.
    •   See Wikipedia.
    •   See Grotjahn, R., and J.J. O'Brien, 1976: Some inaccuracies in finite differencing hyperbolic equations.
  • C080 - Probabilistic prediction in CFD.  Potential interesting articles are given below.
    •
  • C090 - Lotka-Volterra (Predator-Prey) equations (Lotka and Volterra, 1925-1926)

Textbooks referenced on this page, PDFs available free at links below

Library links below give the U.I. Library reference page to the text book.  "PDFs" is the direct link to chapter PDFs.
Note you must be on-campus, connected via VPN to campus networks, or authenticate first, to access textbook chapter PDFs.
  • Arfken, G. B., 2012: Mathematical Methods for Physicists, 7th Ed.  Library link; PDFs.
  • Attenborough, M., 2003: Mathematics for Electrical Engineering and Computing.  Library link; PDFs - use library link.
  • Berry, M.W., et al., eds:  High-performance scientific computing:  algorithms and applications.  Library link
  • Braithwaite, J., 2011:  An Introduction to Hydrodynamics.  (no longer online; see Brian) Notes from hydrodynamics course in Bonn.
  • Bronson, R, and G.B. Costa, 2011:  Schaum's outlines of differential equations, 3rd ed. Library link; PDFs.
  • Cacuci, D.G., I.M. Navon, M. Ionescu-Bujor, 2013:  Computational methods for data evaluation and assimilation.  Library; PDFs.
  • Cushman-Roisin, B., and J.-M. Beckers, 2011:  Intro. to Geophysical Fluid Dynamics.  Library link; PDFs.
  • Charru, F., 2011:  Hydrodynamic Instabilities.  Library link; PDFs.
  • Chibbaro, S., and J.P. Minier, eds, 2014:  Stochastic methods in fluid dynamics.  Library link; PDFs.
  • Despotovic-Zrakic, M., V. Milutinovic, and A. Belic, ed., 2014:  Handbook of research on high performance and
       cloud computing in scientific research and education    .  Library link
  • Durbin, P. A., 2007: Fluid Dynamics with a Computational Perspective.  Library link; PDFs.
  • Durran, D. R., 2010: Numerical Methods for Fluid Dynamics with Applications to Geophysics.  Library link; PDFs
    (earlier edition here.)
  • Durst, F., 2008:  Fluid mechanics: An introduction to the theory of fluid flows.  library link.
  • Eijkhout, V., 2014:  Introduction to High-Performance Scientific Computing.  Home page; PDF/source is here.
  • Emanuel, G., 2001:  Analytical fluid dynamics.  Library link; PDFs.
  • Guinot, V., 2003:  Godunov-type schemes: An introduction for engineers.  Library link; PDFs.
  • Hager, G., and G. Wellein, 2011:  Introduction to High Performance computing for scientists and engineers.  Library link.
  • Holton, J., 2004:  An Introduction to Dynamic Meteorology, 4th ed.  Library link; PDFs.  Also available: 5th edition.
  • Kreiss, H.-O., and J. Lorenz, 1989:  Initial-boundary value problems and the Navier-Stokes equations., Library link; PDFs.
  • Kusse, B., 2006:  Mathematical physics:  Applied Mathematics for Scientists and Engineers.  Library link; PDFs.
  • Kundu, P., I. Cohen, and D. Dowling, 2011:  Fluid Mechanics (5th edition).  Library link; PDFs;
      see also this extensive topic list for an earlier edition.
  • Lahoz, W. B. Khattatov, R. Menard, 2010:  Data assimilation:  Making sense of observations.  Library link; PDFs.
  • Lindzen, R., 1990:  Dynamics in Atmospheric Physics.  Library link; PDFs.
  • Neeman, Henry J., 1996:  Autonomous hierarchical adaptive mesh refinement for multiscale simulations.  Library link; PDF.
  • Plewa, T., T. Linde, and V.G. Weirs, editors, 2003:  Adaptive mesh refinement - theory and applications.  Library link; PDFs.
  • Pozrikidis, C., 2009: Fluid dynamics.  library link.
  • Ross, B., 1986:  An Overview of Numerical Weather Prediction.  PDF.
  • Tu, J., G.H. Yeoh and C. Liu, 2013:  Computational Fluid Dynamics - A practical approach. 2nd Ed.  Library link; PDFs.
  • Watts, R., 2012:  Essentials of applied mathematics for engineers and scientists.  Library link; PDFs.
  • Wesseling, P., 2009:  Principles of Computational Fluid Dynamics.  Library link; PDFs.
  • Wilks, D., 2011:  Statistical Methods in the Atmospheric Sciences, 3rd Ed.  Library link; PDFs.
  • Yaglom, A.; ed. by Uriel Frisch, 2012:  Hydrodynamic Instability and Transition to Turbulence.  Library link; PDFs.

Other textbooks - in UIUC library system (not online)

  • Anderson, D. A., JohnC. Tannehill, and Richard H. Pletcher, 1984:  Computational fluid mechanics
        and heat transfer.      Library link.
  • Bluestein, H. B., 1992:  Synoptic-dynamic meteorology in midlatitudes (vols. I and II).  Library link.
  • Ferziger, J.H., and M. Peric, 2002:  Computational Methods for Engineering Application.  Library link.
  • Kalnay, E., 2003:  Atmospheric modeling, data assimilation, and predictability.  Library link.
  • Lighthill, M. J., 1979:  Waves in Fluids.  Library link.

Journal papers, by author, most free at links below

When given, library links below give the U.I. Library reference page to an article.  "PDFs" is  direct link to manuscript or chapter PDFs.  Most links do not require U.I. authentication - those that do require authentication have "(UIUC)" at the end.