Filtering in the numerical simulation of turbulent compressible flow with sysmmetry preserving discretizations

Abstract

The present thesis investigates how explicit filters can be useful in numerical simulations of turbulent, compressible flow with symmetry preserving discretizations. Such explicit filters provide stability to simulations with shocks, provide stability to low-dissipation schemes on smooth flows and are used as test filters in LES turbulence models such as the Variational Multi-Scale eddy viscosity model or regularization models. The present thesis is a step forward in four main aspects. First, a comparative study of the Symmetry Preserving schemes for compressible flow is conducted. It shows that Rozema’s scheme is more stable and accurate than the other schemes compiled fromthe literature. A sligh tmodification on this scheme is presented and shown to be more stable and accurate in unstructured meshes, but lesser accurate and stable in uniform, structured meshes. Second, a theoretical analysis of the properties of filters for CFD and their consequences on the derivation of the LES equations is conducted. The analysis shows how the diffusive properties of filters are necessary for the consistency of the model. Third, a study of explicit filtering on discrete variables identifies the necessary constraints for the fulfillment of the discrete counterpart of the filter properties. It puts emphases on the different possibilities when requiring the filters to be diffusive. After it, a new family of filters has been derived and tested in newly developed tests that allow the independent study of each property. And last, an algorithm to couple adaptive filtering with time integration is reported and tested on the 2D Isentropic Vortex and on the Taylor-Green vortex problem. Filtering is shown to enhance stability at the cost of locally adding diffusion. This saves the simulations from being diffusive everywhere. The resulting methodology is also shown to be potentially useful for shock-capturing purposes with the simulation of a shock-tube in a fully unstructured mesh.