TRIANGLE BASED ADAPTIVE STENCILS FOR THE SOLUTION OF HYPERBOLIC CONSERVATION-LAWS

A triangle based adaptive difference stencil for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the resulting scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedure. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second-order accuracy. Numerical results for constant and variable coefficient linear advection, as well as for nonlinear flux functions (Burgers' equation and the Buckley-Leverett equation), are presented. The observed order of convergence, after local averaging, is from 1.7 to 2.0 in L1. © 1992.