of all the available data. The weighted-ENO (WENO) schemes by Liu et al. [14] and Jiang and Shu [10] make
A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented. The inter-better use of the available data by defining the interface face value in these schemes is obtained by limiting a higher-order value as a weighted average of the interface values from polynomial reconstruction. The limiting is designed to preserve all stencils. The weights are designed so that in smooth accuracy near extrema and to work well with Runge-Kutta time regions the scheme nearly recovers a very accurate interstepping. Computational efficiency is enhanced by a simple test face value using all stencils but, near discontinuities, it that determines whether the limiting procedure is needed. For linear advection in one dimension, these schemes are shown to be mono-recovers the value from the smoothest stencil. The WENO tonicity-preserving and uniformly high-order accurate. Numerical schemes, however, are still diffusive: they smear discontiexperiments for advection as well as the Euler equations also connuities nearly as much as the ENO schemes.
firm their high accuracy, good shock resolution, and computational
In this paper, we follow the limiting approach. The efficiency. ᮊ 1997 Academic Press interface value is defined by a five-point stencil-the same stencil as the third-order ENO and fifth-order WENO schemes. Compared to PPM, the five-point inter-''smoothest'' data, thereby avoiding interpolations across tions and multi-dimensions are dealt with in Section 3. Numerical experiments appear in Section 4. Finally, con-discontinuities. While an adaptive stencil does avoid spurious oscillations near discontinuities, it does not make use clusions are presented in Section 5. 83