致敬作者: https://surajp92.github.io/
| Index | Description |
|---|---|
| 01 | 1D heat equation: Forward time central space (FTCS) scheme |
| 02 | 1D heat equation: Third-order Runge-Kutta (RK3) scheme |
| 03 | 1D heat equation: Crank-Nicolson (CN) scheme |
| 04 | 1D heat equation: Implicit compact Pade (ICP) scheme |
| 05 | 1D inviscid Burgers equation: WENO-5 with Dirichlet and periodic boundary condition |
| 06 | 1D inviscid Burgers equation: CRWENO-5 with Dirichlet and periodic boundary conditions |
| 07 | 1D inviscid Burgers equation: Flux-splitting approach with WENO-5 |
| 08 | 1D inviscid Burgers equation: Riemann solver approach with WENO-5 using Rusanov solver |
| 09 | 1D Euler equations: Roe solver, WENO-5, RK3 for time integration |
| 10 | 1D Euler equations: HLLC solver, WENO-5, RK3 for time integration |
| 11 | 1D Euler equations: Rusanov solver, WENO-5, RK3 for time integration |
| 12 | 2D Poisson equation: Finite difference fast Fourier transform (FFT) based direct solver |
| 13 | 2D Poisson equation: Spectral fast Fourier transform (FFT) based direct solver |
| 14 | 2D Poisson equation: Fast sine transform (FST) based direct solver for Dirichlet boundary |
| 15 | 2D Poisson equation: Gauss-Seidel iterative method |
| 16 | 2D Poisson equation: Conjugate gradient iterative method |
| 17 | 2D Poisson equation: V-cycle multigrid iterative method |
| 18 | 2D incompressible Navier-Stokes equations (cavity flow): Arakawa, FST, RK3 schemes |
| 19 | 2D incompressible Navier-Stokes equations (vortex merging): Arakawa, FFT, RK3 schemes |
| 20 | 2D incompressible Navier-Stokes equations (vortex merging): Hybrid RK3/CN approach |
| 21 | 2D incompressible Navier-Stokes equations (vortex merging): Pseudospectral solver, 3/2 dealiasing, Hybrid RK3/CN approach |
| 22 | 2D incompressible Navier-Stokes equations (vortex merging): Pseudospectral solver, 2/3 dealiasing, Hybrid RK3/CN approach |
有限差分法核心：
Taylor展开
类似的推导在https://www.youtube.com/watch?v=HMmOk9GIhsw&feature=youtu.be