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Unformatted text preview: Code Validation Demonstrate convergence under spatial mesh refinement x 0 (in 3D, x, y, z 0) Demonstrate convergence as t 0 Compare with science &/or experiment Compare with analytical or approximate solutions (in limiting cases): for example, approximately linear regime of nonlinear problem or Riemann problem for 1D gas dynamics Vary physical parameters (for example, in Burgers' equation, vary viscosity for shock profile solution) Compare with results using other numerical methods & other codes Vary computational parameters (for example, in compressible fluid flow, vary artificial viscosity & CFL factor) Check symmetry & conservation Recommended Methods for Initial Value Problems
Always dynamically adjust t based on an estimate of the local truncation error TRBDF2, especially for stiff problems Fourth-order Runge-Kutta Adams-Bashforth-Moulton predictor-corrector Recommended Methods for PDEs Parabolic PDEs: TRBDF2 for nonlinear diffusion or drift-diffusion; Chorin's method plus predictor-corrector timestep for Navier-Stokes Hyperbolic PDEs: Lax-Wendroff for wave equations; WENO or higherorder Godunov (PPM or CLAWPACK) for gas dynamics; FDTD for Maxwell's equations Elliptic PDEs: For Poisson's equation, banded or sparse direct solvers, or SOR, PCG, or multigrid iterative solvers ...
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This note was uploaded on 03/11/2012 for the course MAT 421 taught by Professor Staff during the Fall '11 term at ASU.
- Fall '11