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Volume V / Solutions and Tests

  1. Exact Solutions
    1. Linear Advection
    2. Circular Advection
    3. Advection-Diffusion Equation
    4. Burgers' Equation
    5. Viscous Burgers' Equation
    6. Traffic Equation
    7. Diffusion Equation
    8. Laplace Equation
    9. Potential Flows
      1. Incompressible Flows
      2. Airfoil Flows
      3. Subsonic Flows
      4. Supersonic Flows
    10. Euler Equations
      1. Simple Waves
      2. Shock Tube Problems (Exact Riemann Solver)
      3. Normal/Oblique Shock Waves
      4. Flow over a Cylinder
      5. Ringleb's Flow
    11. Navier-Stokes Equations
      1. Flat Plate Boudnary Layer
      2. Hypersonic Heat Transfer
    12. MHD Equations
      1. Simple Wave Solutions
      2. MHD Nozzle Flows
  2. General Solutions and Extrapolations
    1. General Simple Wave Solutions
    2. Richardson's Extrapolation
  3. Accessary
    1. von Neumann Stability Analysis
    2. Error Analysis
  4. Test Problems
    1. Sod's Shock Tube
    2. Two Interacting Blastwaves
    3. Einfeldt Strong Rarefaction Test
    4. Shu and Osher Shocktube
    5. Entropy wave
    6. Shock Diffraction
    7. Double Mach Reflection
    8. Supersonic Forward-Facing Step Flow
    9. ONERA M6 Wing
    10. NACA Airfoil
    11. RAE Airfoil
    12. Shock Reflection
    13. Brio and Wu (1984)
    14. Torsional alfven wave
    15. Orzag-Tang Vortex
    16. Shock Instability Problems
    17. Carbuncle

Volume I / Governing Equations

  1. Part I Scalar Equations
    1. Linear Advection Equations
      1. 1D
      2. 2D
      3. 3D
    2. Burgers' Equation and KdV Equation
      1. 1D
      2. 2D
      3. 3D
    3. Diffusion Equation
      1. 1D
      2. 2D
      3. 3D
    4. Advection-Diffusion Equation
      1. 1D
      2. 2D
      3. 3D
    5. Advection-Reaction Equation
      1. 1D
      2. 2D
      3. 3D
    6. Reaction-Diffusion Equation
      1. 1D
      2. 2D
      3. 3D
    7. Poisson Equation
      1. 1D
      2. 2D
      3. 3D
  2. Part II Systems of Equations
    1. Euler Equations
      1. 1D
      2. 2D
      3. 3D
    2. Polytropic Euler Equations
      1. 1D
      2. 2D
      3. 3D
    3. Isothermal Euler Equations
      1. 1D
      2. 2D
      3. 3D
    4. Shallow water Equations
      1. 1D
      2. 2D
      3. 3D
    5. MHD Equations
      1. 1D Polytrope MHD
      2. 2D Adiabatic MHD
      3. 3D Adiavatic MHD
        1. Linear Eigensystem
        2. Renormalized Eigensystem
      4. 3D Isothermal MHD
    6. Resistive MHD
      1. Magnetic Relnolds Number
      2. Eight wave formalism
    7. Navier-Stokes Equations
      1. 1D
      2. 2D
      3. 3D
        1. Reynolds Number
        2. Prandtl Number
        3. Dissipation Function
    8. Moment Equations
    9. Lagrangian fluid
    10. Stiff relaxation
    11. Geometrical Source Terms and Tips for Fininte Volume Discretization
      1. 1D Cylindrical Coordinate
      2. 1D Spherical Coordinate
      3. 2D Isothermal Disk
        1. Angular momentum conservation form

Volume II / Method of Discretization

  1. Finite Volume Method
    1. Numerical Flux
  2. Finite Difference Method
  3. Finite Element Method
    1. Discontinuous Galerkin
  4. Spectral Difference Method
  5. Spectral Volume Method
  6. Operator Splitting
    1. Godunov Spritting
    2. Strang Splitting
  7. Accessories
    1. CFL number
    2. Artificial Viscosity
    3. Entropy fix

Volume III / Numerical Flux and Riemann Problem

  1. Lax-Friedrich/Local Lax-Friedlich
  2. HLL
  3. ASUM
  4. Roe
    1. Nature of Roe average
    2. Property U
    3. Entropy fix
    4. Positivity condition
  5. Exact Riemann Solver
    1. Two Shock Approximation

Volume IV / High Order Scheme

  1. Part I Temporal High Order
    1. TVD Runge-Kutta
    2. High-Frequency dumping
  2. Part II Spatial High Order
    1. MUSCL-type scheme
      1. TVD Limiter
        1. minmod
        2. double minmod
        3. van Leer limiter
        4. Superbee limiter
        5. van Albada limiter
        6. van Albada2
      2. TVB Limiter
    2. van Leer's kappa Scheme
    3. PPM
    4. ENO/WENO
    5. RKDG
    6. CIP

Volume VI / Techniques to get Steady Solutions

  1. Three time stepping
  2. Preconditioning
  3. Multigrid Iteration
  4. Rung-Kutta for High-frequency Dumping
  5. Dual timestepping

Volume VII / Beyond the Divergence Free Method

  1. Eight wave
  2. Projection
  3. Constraint Transport (CT)
  4. Locally divergence free basis function for DG

uncategolyzed topics

  1. SPH
  2. coding tips
    1. fortran90
    2. MPI