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

A new low-dissipation low-dispersion second-order scheme suitable for unstructured finite volume flow solvers is presented that 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 information for computing face values of the fluxes and to use this additional degree of freedom to improve the dispersion properties of the scheme. The scheme is motivated 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-resolvin...

[1]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[2]  Parviz Moin,et al.  ADVANCES IN LARGE EDDY SIMULATION METHODOLOGY FOR COMPLEX FLOWS , 2002, Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena.

[3]  Martine Baelmans,et al.  A Finite Volume Formulation for Compact Schemes with Applications to LES , 2001 .

[4]  Eli Turkel,et al.  Assessment of Preconditioning Methods , 1995 .

[5]  P. Moin,et al.  On the Effect of Numerical Errors in Large Eddy Simulations of Turbulent Flows , 1997 .

[6]  P. Moin,et al.  A numerical method for large-eddy simulation in complex geometries , 2004 .

[7]  Werner Haase,et al.  Progress in Hybrid RANS-LES Modelling , 2010 .

[8]  Christopher K. W. Tam,et al.  Direct computation of nonlinear acoustic pulses using high-order finite difference schemes , 1993 .

[9]  J. C. Kok,et al.  A high-order low-dispersion symmetry-preserving finite-volume method for compressible flow on curvilinear grids , 2009, J. Comput. Phys..

[10]  R. C. Swanson,et al.  On Central-Difference and Upwind Schemes , 1992 .

[11]  Parviz Moin,et al.  A Recommended Modification to the Dynamic Two-Parameter Mixed Subgrid Scale Model , 2001 .

[12]  Axel Probst,et al.  Scale-Resolving Simulations of Wall-Bounded Flows with an Unstructured Compressible Flow Solver , 2015 .

[13]  Axel Probst,et al.  Scale-Resolving Simulations with a Low-Dissipation Low-Dispersion Second-Order Scheme for Unstructured Finite-Volume Flow Solvers , 2015 .

[14]  Antony Jameson,et al.  Structural Wall-modeled LES Using a High-order Spectral Difference Scheme for Unstructured Meshes , 2014 .

[15]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[16]  Tobias Knopp,et al.  Enhancement of an industrial finite-volume code for large-eddy-type simulation of incompressible high Reynolds number flow using near-wall modelling , 2010 .

[17]  S. Ghosal.  An Analysis of Numerical Errors in Large-Eddy Simulations of Turbulence , 1996 .

[18]  Ronald J. Adrian,et al.  Hairpin vortex organization in wall turbulencea) , 2007 .

[19]  Miguel R. Visbal,et al.  On the use of higher-order finite-difference schemes on curvilinear and deforming meshes , 2002 .

[20]  J. Debonis.  Solutions of the Taylor-Green Vortex Problem Using High-Resolution Explicit Finite Difference Methods , 2013 .

[21]  Rémi Abgrall,et al.  High‐order CFD methods: current status and perspective , 2013 .

[22]  Ralf Heinrich,et al.  The DLR TAU-Code: Recent Applications in Research and Industry , 2006 .

[23]  Marc Garbey,et al.  Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation , 2005 .

[24]  Miguel R. Visbal,et al.  Turbulence spectra characteristics of high order schemes for direct and large eddy simulation , 2001 .

[25]  Krishnan Mahesh,et al.  Analysis of numerical errors in large eddy simulation using statistical closure theory , 2007, J. Comput. Phys..