On a large time-step high resolution scheme
Mathematics of Computation
Journal of Computational Physics
Flux difference splitting and the balancing of source terms and flux gradients
Journal of Computational Physics
Large time step shock-capturing techniques for scalar conservation laws
Large time step shock-capturing techniques for scalar conservation laws
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A class of large time step Godunov schemes for hyperbolic conservation laws and applications
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
It is possible to relax the Courant-Friedrichs-Lewy condition over the time step when using explicit schemes. This method, proposed by Leveque, provides accurate and correct solutions of non-sonic shocks. Rarefactions need some adjustments which are explored in the present work with scalar equation and systems of equations. The non-conservative terms that appear in systems of conservation laws introduce an extra difficulty in practical application. The way to deal with source terms is incorporated into the proposed procedure. The boundary treatment is analysed and a reflection wave technique is considered. In presence of strong discontinuities or important source terms, a strategy is proposed to control the stability of the method allowing the largest time step possible. The performance of the above scheme is evaluated to solve the homogeneous shallow water equations and the shallow water equations with source terms.