Non-oscillatory Central Differencing for Hyperbolic Conservation Laws

Many of the recently developed high-resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the “direction of the wind.” Instead, we propose to use as a building block the more robust Lax-Friedrichs (LxF) solver. The main advantage is simplicity: no Riemann problems are solved and hence field-by-field decompositions are avoided. The main disadvantage is the excessive numerical viscosity typical to the LxF solver. We compensate for it by using high-resolution MUSCL-type interpolants. Numerical experiments show that the quality of the results obtained by such convenient central differencing is comparable with those of the upwind schemes. c ©Academic Press, Inc.