Flux-Corrected Pseudospectral Method for Scalar Hyperbolic Conservation Laws
Abstract
The pseudospectral method has under-used advantages in problems involving shocks and discontinuities. These emerge from superior accuracy in phase and group velocities as compared to finite difference schemes of all orders. Dispersion curves for finite difference schemes suggest that group velocity error typically outranks Gibbs' error as a cause of numerical oscillation. A flux conservative form of the pseudospectral method is derived for compatibility with flux limiters used to preserve monotonicity. The resulting scheme gives high quality results in linear advection and shock formation/propagation examples.
- Publication:
-
Journal of Computational Physics
- Pub Date:
- June 1989
- DOI:
- 10.1016/0021-9991(89)90056-9
- Bibcode:
- 1989JCoPh..82..413M
- Keywords:
-
- Computational Fluid Dynamics;
- Conservation Laws;
- Hyperbolic Functions;
- Scalars;
- Shock Wave Propagation;
- Spectral Methods;
- Advection;
- Burger Equation;
- Finite Difference Theory;
- Group Velocity;
- Inviscid Flow;
- Linear Equations;
- Phase Error;
- Shock Wave Generators;
- Fluid Mechanics and Heat Transfer