TY - JOUR

T1 - A robust, colocated, implicit algorithm for direct numerical simulation of compressible, turbulent flows

AU - Hou, Yucheng

AU - Mahesh, Krishnan

PY - 2005/5/1

Y1 - 2005/5/1

N2 - A non-dissipative, robust, implicit algorithm is proposed for direct numerical and large-eddy simulation of compressible turbulent flows. The algorithm addresses the problems caused by low Mach numbers and under-resolved high Reynolds numbers. It colocates variables in space to allow easy extension to unstructured grids, and discretely conserves mass, momentum and total energy. The Navier-Stokes equations are non-dimensionalized using an incompressible scaling for pressure, and the energy equation is used to obtain an expression for the velocity divergence. A pressure-correction approach is used to solve the resulting equations, such that the discrete divergence is constrained by the energy equation. As a result, the discrete equations analytically reduce to the incompressible equations at very low Mach number, i.e., the algorithm overcomes the acoustic time-scale limit without preconditioning or solution of an implicit system of equations. The algorithm discretely conserves kinetic energy in the incompressible inviscid limit, and is robust for inviscid compressible turbulence on the convective time-scale. These properties make it well-suited for DNS/LES of compressible turbulent flows. Results are shown for acoustic propagation, the incompressible Taylor problem, periodic shock tube problem, and isotropic turbulence.

AB - A non-dissipative, robust, implicit algorithm is proposed for direct numerical and large-eddy simulation of compressible turbulent flows. The algorithm addresses the problems caused by low Mach numbers and under-resolved high Reynolds numbers. It colocates variables in space to allow easy extension to unstructured grids, and discretely conserves mass, momentum and total energy. The Navier-Stokes equations are non-dimensionalized using an incompressible scaling for pressure, and the energy equation is used to obtain an expression for the velocity divergence. A pressure-correction approach is used to solve the resulting equations, such that the discrete divergence is constrained by the energy equation. As a result, the discrete equations analytically reduce to the incompressible equations at very low Mach number, i.e., the algorithm overcomes the acoustic time-scale limit without preconditioning or solution of an implicit system of equations. The algorithm discretely conserves kinetic energy in the incompressible inviscid limit, and is robust for inviscid compressible turbulence on the convective time-scale. These properties make it well-suited for DNS/LES of compressible turbulent flows. Results are shown for acoustic propagation, the incompressible Taylor problem, periodic shock tube problem, and isotropic turbulence.

KW - All-Mach number

KW - Compressible turbulence

KW - Direct numerical simulation

KW - Discrete energy conservation

KW - Large-eddy simulation

KW - Non-dissipative

UR - http://www.scopus.com/inward/record.url?scp=16844363667&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=16844363667&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2004.10.039

DO - 10.1016/j.jcp.2004.10.039

M3 - Article

AN - SCOPUS:16844363667

VL - 205

SP - 205

EP - 221

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 1

ER -