Non-oscillatory Central Differencing for Hyperbolic Conservation Laws Haim Nessyahu and Eitan Tadmor

Many of the recently developed high-resolution schemes for hyperbolic conservation laws are based on upwind di erencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the eld-byeld 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 eld-byeld 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 di erencing is comparable with those of the upwind schemes. c Academic Press, Inc.