UPWIND FINITE-VOLUME METHOD WITH A TRIANGULAR MESH FOR CONSERVATION-LAWS

A new upwind scheme has been developed and analyzed for a finite-volume solution of the conservation laws on triangular meshes. The scheme is an upwind second-order extrapolation with simple local limiters, and it is weakly second-order accurate and satisfies maximum principles. In one dimension, the scheme reduces to a fully upwind second-order scheme with a simple local limiter. Preliminary numerical results demonstrating the performance of the scheme on a variety of initial-boundary value problems are presented. The order of convergence of the scheme is found to vary from 1.6 to 1.9 in L1. © 1993 by Academic Press, Inc.