On the properties of discrete spatial filters for CFD

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/The spatial filtering of variables in the context of Computational Fluid Dynamics (CFD) is a common practice. Most of the discrete filters used in CFD simulations are locally accurate models of continuous operators. However, when filters are adaptative, i.e. the filter width is not constant, or meshes are irregular, discrete filters sometimes break relevant global properties of the continuous models they are based on. For example, the principle of maxima and minima reduction or conservation are eventually infringed. In this paper, we analyze the properties of analytic continuous convolution filters and extract those we consider to define filtering. Then, we impose the accomplishment of these properties on explicit discrete filters by means of constraints. Three filters satisfying the derived conditions are deduced and compared to common differential discrete CFD filters on synthetic fields. Tests on the developed discrete filters show the fulfillment of the imposed properties. In particular, the problem of maxima and minima generation is resolved for physically relevant cases. The tests are conducted on the basis of the eigenvectors of graph Laplacian matrices of meshes. Thus, insight into the relations between filtering and oscillation growth on general meshes is provided. Further tests on singularity fields and on isentropic vortices have also been conducted to evaluate the performance of filters on basic CFD fields. Results confirm that imposing the proposed conditions makes discrete filters properties consistent with those of the continuous ones.Peer ReviewedPostprint (author's final draft

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

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.Postprint (published version

CFD modeling of a fixed-bed biofilm reactor coupling hydrodynamics and biokinetics

Peer ReviewedPostprint (author's final draft