---- *** Volume I / Governing Equations +Part I Scalar Equations ++Linear Advection Equations +++1D +++2D +++3D ++Burgers' Equation and KdV Equation +++1D +++2D +++3D ++Diffusion Equation +++1D +++2D +++3D ++Advection-Diffusion Equation +++1D +++2D +++3D ++Advection-Reaction Equation +++1D +++2D +++3D ++Reaction-Diffusion Equation +++1D +++2D +++3D ++Poisson Equation +++1D +++2D +++3D +Part II Systems of Equations ++Euler Equations +++1D +++2D +++3D ++Polytropic Euler Equations +++1D +++2D +++3D ++Isothermal Euler Equations +++1D +++2D +++3D ++Shallow water Equations +++1D +++2D +++3D ++MHD Equations +++1D Polytrope MHD +++2D Adiabatic MHD +++3D Adiavatic MHD ++++Linear Eigensystem ++++Renormalized Eigensystem +++3D Isothermal MHD ++Resistive MHD +++Magnetic Relnolds Number +++Eight wave formalism ++Navier-Stokes Equations +++1D +++2D +++3D ++++Reynolds Number ++++Prandtl Number ++++Dissipation Function ++Moment Equations ++Lagrangian fluid ++Stiff relaxation ++Geometrical Source Terms and Tips for Fininte Volume Discretization +++1D Cylindrical Coordinate +++1D Spherical Coordinate +++2D Isothermal Disk ++++Angular momentum conservation form ---- *** Volume II / Method of Discretization +Finite Volume Method ++Numerical Flux +Finite Difference Method +Finite Element Method ++Discontinuous Galerkin +Spectral Difference Method +Spectral Volume Method +Operator Splitting ++Godunov Spritting ++Strang Splitting +Accessories ++CFL number ++Artificial Viscosity ++Entropy fix ---- *** Volume III / Numerical Flux and Riemann Problem +Lax-Friedrich/Local Lax-Friedlich +HLL +ASUM +Roe ++Nature of Roe average ++Property U ++Entropy fix ++Positivity condition +Exact Riemann Solver ++Two Shock Approximation ---- *** Volume IV / High Order Scheme +Part I Temporal High Order ++TVD Runge-Kutta ++High-Frequency dumping +Part II Spatial High Order ++MUSCL-type scheme +++TVD Limiter ++++minmod ++++double minmod ++++van Leer limiter ++++Superbee limiter ++++van Albada limiter ++++van Albada2 +++TVB Limiter ++van Leer's kappa Scheme ++PPM ++ENO/WENO ++RKDG ++CIP ---- *** Volume V / Solutions and Tests +Exact Solutions and Extrapolations for Accuracy Study ++Linear Advection ++Laplace Equation ++Cauchy-Riemann Equations (Potential Flows) ++Simple Waves ++Euler Equations ++Richardson's Extrapolation +Accessary ++von Neumann Stability Analysis ++Error Analysis +Test Problems ++Sod's Shock Tube ++Two Interacting Blastwaves ++Einfeldt Strong Rarefaction Test ++Shu and Osher Shocktube ++Entropy wave ++Shock Diffraction ++Double Mach Reflection ++Brio and Wu (1984) ++Torsional alfven wave ++Orzag-Tang Vortex ++Carbuncle ---- *** Volume VI / Techniques to get Steady Solutions +Three time stepping +Preconditioning +Multigrid Iteration +Rung-Kutta for High-frequency Dumping +Dual timestepping ---- *** Volume VII / Beyond the Divergence Free Method +Eight wave +Projection +Constraint Transport (CT) +Locally divergence free basis function for DG ---- *** uncategolyzed topics +SPH +coding tips ++fortran90 ++MPI
