TY - JOUR

T1 - A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows

AU - Subbareddy, Pramod K

AU - Candler, Graham V

PY - 2009/3/20

Y1 - 2009/3/20

N2 - A robust, implicit, low-dissipation method suitable for LES/DNS of compressible turbulent flows is discussed. The scheme is designed such that the discrete flux of kinetic energy and its rate of change are consistent with those predicted by the momentum and continuity equations. The resulting spatial fluxes are similar to those derived using the so-called skew-symmetric formulation of the convective terms. Enforcing consistency for the time derivative results in a novel density weighted Crank-Nicolson type scheme. The method is stable without the addition of any explicit dissipation terms at very high Reynolds numbers for flows without shocks. Shock capturing is achieved by switching on a dissipative flux term which tends to zero in smooth regions of the flow. Numerical examples include a one-dimensional shock tube problem, the Taylor-Green problem, simulations of isotropic turbulence, hypersonic flow over a double-cone geometry, and compressible turbulent channel flow.

AB - A robust, implicit, low-dissipation method suitable for LES/DNS of compressible turbulent flows is discussed. The scheme is designed such that the discrete flux of kinetic energy and its rate of change are consistent with those predicted by the momentum and continuity equations. The resulting spatial fluxes are similar to those derived using the so-called skew-symmetric formulation of the convective terms. Enforcing consistency for the time derivative results in a novel density weighted Crank-Nicolson type scheme. The method is stable without the addition of any explicit dissipation terms at very high Reynolds numbers for flows without shocks. Shock capturing is achieved by switching on a dissipative flux term which tends to zero in smooth regions of the flow. Numerical examples include a one-dimensional shock tube problem, the Taylor-Green problem, simulations of isotropic turbulence, hypersonic flow over a double-cone geometry, and compressible turbulent channel flow.

KW - Compressible flow

KW - Direct numerical simulation

KW - Fully discrete

KW - Implicit time integration

KW - Kinetic energy

KW - Large-eddy simulation

KW - Non-dissipative

UR - http://www.scopus.com/inward/record.url?scp=58649086284&partnerID=8YFLogxK

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U2 - 10.1016/j.jcp.2008.10.026

DO - 10.1016/j.jcp.2008.10.026

M3 - Article

AN - SCOPUS:58649086284

VL - 228

SP - 1347

EP - 1364

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 5

ER -