On Convergence of Finite-Difference Shock-Capturing Schemes in Regions of Shock Waves Influence

Abstract We perform a comparative accuracy study of the Rusanov, CABARETM, and WENO5 difference schemes used to compute dam break problem for shallow water theory equations. demonstrate that all three have first order convergence inside region occupied by centered rarefaction wave, Rusanov scheme has second in area constant flow between shock while CABARETM there is no local this area. This due fact numerical solutions obtained undamped oscillations influence shock, amplitude which does not decrease with decreasing grid steps. As result, taking into account Lax-Wendroff theorem, conservative converge only weakly exact solution contrast scheme, locally converges region.