A simple extended compact nonlinear scheme with adaptive dissipation control

Abstract

Weighted compact nonlinear schemes (WCNSs) [1] are a popular family of high resolution shock-capturing methods, of which the nonlinear interpolation procedure is essential for non-oscillatory shock-capturing computation. In this article, numerical dissipation of an improved compact nonlinear scheme, which is fifth-order accurate, is significantly reduced by further introducing a six-point optimized stencil in the nonlinear interpolation, without using more complex local or global smoothness indicators. Nonlinear dissipation and dispersion are then further reduced by using an adaptive strategy. In particular, the computational procedure including the proposed six-point nonlinear interpolation is almost the same as that of the improved five-point scheme, and thus their computational efforts are similar. However, significant gains in numerical performance are obtained while including the six-point optimized stencil. Benchmark cases in one and two space dimensions are used to assess performance of the present scheme, viz., shock-capturing capability and resolution in smooth regions, showing promising advantages.