A symmetry-preserving discretisation and regularisation model for compressible flow with application to turbulent channel flow |
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Authors: | W Rozema JC Kok RWCP Verstappen AEP Veldman |
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Institution: | 1. Johann Bernoulli Institute for Mathematics and Computer Science, Faculty of Mathematics and Natural Sciences, University of Groningen, Groningen, The Netherlands;2. Flight Physics &3. Loads, Aerospace Vehicles, National Aerospace Laboratory NLR, Amsterdam, The Netherlandswybe.rozema@nlr.nl;5. Flight Physics &6. Loads, Aerospace Vehicles, National Aerospace Laboratory NLR, Amsterdam, The Netherlands |
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Abstract: | Most simulation methods for compressible flow attain numerical stability at the cost of swamping the fine turbulent flow structures by artificial dissipation. This article demonstrates that numerical stability can also be attained by preserving conservation laws at the discrete level. A new mathematical explanation of conservation in compressible flow reveals that many conservation properties of convection are due to the skew-symmetry of the convection operator. By preserving this skew-symmetry at the discrete level, a fourth-order accurate collocated symmetry-preserving discretisation with excellent conservation properties is obtained. Also a new symmetry-preserving regularisation subgrid-scale model is proposed. The proposed techniques are assessed in simulations of compressible turbulent channel flow. The symmetry-preserving discretisation for compressible flow has good stability without artificial dissipation and yields acceptable results already on coarse grids. Regularisation does not consistently improve upon no-model results, but often compares favourably with eddy-viscosity models. |
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Keywords: | skew-symmetric discretisation discrete conservation large-eddy simulation regularisation modelling compressible flow |
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