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

An open and parallel multiresolution framework using block-based adaptive grids

A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and explicit time integration. Grid refinement and coarsening are triggered by multiresolution analysis, i.e. thresholding of wavelet coefficients, which allow controlling the precision of the adaptive approximation of the solution with respect to uniform grid computations. The implementation of the scheme is fully parallel using MPI with a hybrid data structure. Load balancing relies on space filling curves techniques. Validation tests for 2D advection equations allow to assess the precision and performance of the developed code. Computations of the compressible Navier-Stokes equations for a temporally developing 2D mixing layer illustrate the properties of the code for nonlinear multi-scale problems. The code is open source

A Discontinuity-Capturing Methodology for Two-Phase Inviscid Compressible Flow

The explicit filtering approach is applied to the quasi-conservative five-equation model of compressible two-phase flows to capture the interface between each fluid and a shock wave. The basic idea of the present filter is to combine a low-order linear filter with a high-order one via a proper discontinuity sensor and optimum linear weights. The capability of the proposed filter in capturing the contact discontinuity and damping the grid-to-grid oscillations is analysed. Various one-dimensional and two-dimensional test cases are performed, namely the interface advection of gas-gas flow, the shockinterface interaction, the gas-liquid Riemann problem, and the inviscid shock-bubble interaction. The numerical results reveal that the present filtering method can accurately capture the propagation of the shock waves and interfaces. Additionally, it produces less spurious oscillations compared with the existing 2nd-order discontinuity-capturing filter

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

Passive noise control strategies for jets exhausting over flat surfaces : an LES study

Unconventional aircraft propulsion configurations have to be considered in the future to address environmental issues, including air traffic noise that is know to affect communities surrounding airports. One approach involves rectangular jets in the vicinity of flat surfaces that are parallel to the jet axis in an attempt to shield the noise, but previous experimental work indicated that there is an increase in the noise generated by these configurations, mainly associated with the effect that the plate trailing edge exerts on the flow. In this work, we use large eddy simulations to investigate the potential of wall deformations at the plate trailing edge to reduce jet noise. We consider a high aspect ratio rectangular nozzle exhausting a jet over a flat surface in different configurations, and estimate the farfield noise using the Ffowcs Williams and Hawkins acoustic analogy. Because of the high aspect ratio of the rectangular nozzle, we approximate the jet as being two-dimensional, and use periodic boundary conditions in the spanwise direction. For the configurations that we considered here, the trailing edge deformations did not seem to affect the noise significantly; an overall sound pressure level in the order of 1-2 dB was observed for some selected cases

Comparison of Subgrid-scale Viscosity Models and Selective Filtering Strategy for Large-eddy Simulations

Explicitly filtered large-eddy simulations (LES), combining high-accuracy schemes with the use of a selective filtering without adding an explicit subgrid-scales (SGS) model, are carried out for the Taylor-Green-vortex and the supersonic-boundary-layer cases. First, the present approach is validated against direct numerical simulation (DNS) results. Subsequently, several SGS models are implemented in order to investigate if they can improve the initial filter-based methodology. It is shown that the most accurate results are obtained when the filtering is used alone as an implicit model, and for a minimal cost. Moreover, the tests for the Taylor-Green vortex indicate that the discretization error from the numerical methods, notably the dissipation error from the high-order filtering, can have a greater influence than the SGS models

Assessment of a high-order shock-capturing central-difference scheme for hypersonic turbulent flow simulations

High-speed turbulent flows are encountered in most space-related applications (including exploration, tourism and defense fields) and represent a subject of growing interest in the last decades. A major challenge in performing high-fidelity simulations of such flows resides in the stringent requirements for the numerical schemes to be used. These must be robust enough to handle strong, unsteady discontinuities, while ensuring low amounts of intrinsic dissipation in smooth flow regions. Furthermore, the wide range of temporal and spatial active scales leads to concurrent needs for numerical stabilization and accurate representation of the smallest resolved flow scales in cases of under-resolved configurations. In this paper, we present a finite-difference high-order shock-capturing technique based on Jameson's artificial diffusivity methodology. The resulting scheme is ninth-order-accurate far from discontinuities and relies on the addition of artificial dissipation close to large gradients. The shock detector is slightly revised to enhance its selectivity and avoid spurious activations of the shock-capturing term. A suite of test cases ranging from 1D to 3D configurations (namely, shock tubes, Shu-Osher problem, isentropic vortex advection, under-expanded jet, compressible Taylor-Green Vortex, supersonic and hypersonic turbulent boundary layers) is analysed in order to test the capability of the proposed numerical strategy to handle a large variety of problems, ranging from calorically-perfect air to multi-species reactive flows. Results obtained on under-resolved grids are also considered to test the applicability of the proposed strategy in the context of implicit Large-Eddy Simulations