A Speed-Up Strategy for Finite Volume WENO Schemes for Hyperbolic Conservation Laws

In this paper, a speed-up strategy for finite volume WENO schemes is developed for solving hyperbolic conservation laws. It adopts p-adaptive like reconstruction, which automatically adjusts from fifth order WENO reconstruction to first order constant reconstruction when nearly constant solutions are detected by the undivided differences. The corresponding order of accuracy for the solutions is shown to be the same as obtained by original WENO schemes. The strategy is implemented with both WENO and mapped WENO schemes. Numerical examples in different space dimensions show that the strategy can reduce the computational cost by 20–40%, especially for problems with large fraction of constant regions.