A Low-Dissipation Low-Dispersion Second-Order Scheme for Unstructured Finite-Volume Flow Solvers

Abstract

A new low-dissipation low-dispersion second-order scheme suitable for unstructured finite-volume flow solvers is presented which is designed for vortical flows and for scale-resolving simulations of turbulence. The idea is that, by optimizing its dispersion properties, a standard second-order method can be improved significantly for such flows. The key is to include gradient in formation for computing face-values of the fluxes and to use this additional degree of freedom to improve the dispersion properties of the scheme. We motivate the scheme by a theoretical consideration of the dispersion properties for a one-dimensional scalar transport equation problem. Then the new scheme is applied using the DLR TAU-code for compressible flows and the DLR THETA-code for incompressible flows for simulations of the moving vortex problem and the Taylor-Green vortex flow. The improved accuracy for small scale transportation and the easy implementation make this scheme a promising candidate for efficient scale-resolving simulations of turbulent flows. Note: This paper is jointly published with a companion paper by Probst et al., where the low-dissipation low-dispersion 2nd-order scheme is applied to scale-resolving simulations of a channel flow, the backward-facing step flow, the flow around a rudimentary landing gear and around a 3-element airfoil near stall.