Linear high-resolution schemes for hyperbolic conservation laws: TVB numerical evidence

The Osher-Chakrabarthy family of linear flux-modification schemes is considered. Improved lower bounds on the compression factors are provided, which suggest the viability of using the unlimited version. The LLF flux formula is combined with these schemes in order to obtain compact finite-difference algorithms. The resulting schemes are applied to a battery of numerical tests, going from advection and Burgers equations to Euler and MHD equations, including the Orszag-Tang 2D vortex problem. Total-variation-bounded behavior is evident in all cases, even with time-independent upper bounds. The proposed schemes, however, do not deal properly with compound shocks, arising from non-convex fluxes, as shown by Buckley-Leverett test simulations. Ministry of Science and the Balearic Islands Government 2 C. Bona acknowledges the Charles University in Prague for his hospitality during the completion of this work and specially Tomas Ledvinka for useful suggestions and discussions.