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Following the previous work of Qiu and Shu (SIAM J Sci Comput 31: 584–607, 2008), we investigate the performance of Hermite weighted essentially non-oscillatory (HWENO) scheme for nonconvex conservation laws. Similar to many other high order methods, we show that the finite volume HWENO scheme performs poorly for some nonconvex conservation laws. We modify the scheme around the nonconvex regions,...
In this paper, we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory (HWENO) schemes based on the work (Computers & Fluids, 34: 642–663 (2005)) by Qiu and Shu, with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws. The key idea of HWENO is to evolve both with the solution...
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