Optimization of weighted ENO schemes for DNS of compressible turbulence

Abstract

A family of weighted ENO schemes is assessed for direct numerical simulations of compressible turbulence. Analysis and computational experiments show the schemes are limited for this application because of the numerical dissipation they introduce. The damping has two sources: the upwinded, optimal difference stencils, and the smoothness measurement. Bandwidth optimization techniques are used to develop symmetric optimal stencils with reduced dissipation and greater resolving efficiency. In particular a third-order, 6point stencil and a fourth-order, 8-point stencil are obtained. Numerical testing validates the optimization. When the bandwidth-optimized stencils replace their order-optimized counterparts in the weighted ENO schemes, the smoothness measurement remains a source of dissipation. However, numerical experiments demonstrate that the bandwidth-optimized stencils improve the performance of the weighted ENO scheme.