Multigrid Convergence Acceleration for Turbulent Supersonic Flows

A multigrid convergence acceleration technique has been developed for solving both the Navier-Stokes and turbulence transport equations. For turbulence closure a low-Reynolds-number q-ω turbulence model is employed. To enable convergence, the stiff non-linear turbulent source terms have to be treated in a special way. Further modifications to standard multigrid methods are necessary for the resolution of shock waves in supersonic flows. An implicit LU algorithm is used for numerical time integration. Several ramped duct test cases are presented to demonstrate the improvements in performance of the numerical scheme. Cases with strong shock waves and separation are included. It is shown to be very effective to treat fluid and turbulence equations with the multigrid method.

[1]  J. Shuen,et al.  Upwind differencing and LU factorization for chemical non-equilibrium Navier-Stokes equations , 1992 .

[2]  T. J. Coakley,et al.  Turbulence modeling methods for the compressible Navier-Stokes equations , 1983 .

[3]  Jack Edwards,et al.  Development of an upwind relaxation multigrid method for computing three-dimensional, viscous internal flows , 1995 .

[4]  Gary S. Settles,et al.  Details of a Shock-Separated Turbulent Boundary Layer at a Compression Corner , 1976 .

[5]  Alexander J. Smits,et al.  Turbulence structure in a shock wave/turbulent boundary-layer interaction , 1989 .

[6]  A. Arnone,et al.  Navier-Stokes turbine heat transfer predictions using two-equation turbulence , 1992 .

[7]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[8]  Rolf Radespiel,et al.  Progress with multigrid schemes for hypersonic flow problems , 1995 .

[9]  J. Yokota.  A diagonally inverted LU implicit multigrid scheme for the 3-D Navier-Stokes equations and a two equation model of turbulence , 1989 .

[10]  Jack R. Edwards,et al.  An Implicit Multigrid Algorithm for Computing Hypersonic, Chemically Reacting Viscous Flows , 1996 .

[11]  Seokkwan Yoon,et al.  Numerical study of chemically reacting flows using a lower-upper symmetric successive overrelaxation scheme , 1989 .

[12]  Dochan Kwak,et al.  Multigrid convergence of an implicit symmetric relaxation scheme , 1993 .

[13]  Alexander J. Smits,et al.  A Survey of Measurements and Measuring Techniques in Rapidly Distorted Compressible Turbulent Boundary Layers , 1989 .

[14]  Eli Turkel,et al.  Extension of multigrid methodology to supersonic/hypersonic 3‐D viscous flows , 1993 .

[15]  B. Stoufflet,et al.  Characteristic multigrid method application to solve the Euler equations with unstructured and unnested grids , 1993 .

[16]  P. Wesseling,et al.  A multigrid method for the compressible Navier-Stokes equations , 1986 .

[17]  Jack R. Edwards.  Upwind relaxation multigrid method for computing three-dimensional, viscous internal flows , 1996 .

[18]  W. Mulder.  A high-resolution Euler solver based on multigrid, semi-coarsening, and defective correction , 1992 .

[19]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[20]  Eli Turkel,et al.  On Central-Difference and Upwind Schemes , 1992 .

[21]  E. Turkel,et al.  An effective multigrid method for high-speed flows , 1992 .

[22]  D. Wilcox.  Reassessment of the scale-determining equation for advanced turbulence models , 1988 .

[23]  Gary S. Settles,et al.  Detailed Study of Attached and Separated Compression Corner Flowfields in High Reynolds Number Supersonic Flow , 1979 .

[24]  C. G. Speziale,et al.  Critical Evaluation of Two-Equation Models for Near-Wall Turbulence , 1992 .

[25]  P. Gerlinger,et al.  Numerical simulation of mixing for turbulent slot injection , 1996 .

[26]  G. Gerolymos.  Implicit multiple-grid solution of the compressible Navier-Stokes equations using k-epsilon turbulence closure , 1990 .

[27]  P. Gerlinger,et al.  Numerical simulation of supersonic combustion problems using an implicit LU-SGS scheme and k-epsilon/q-omega turbulence closure , 1993 .

[28]  Dieter Brüggemann,et al.  Matrix dissipation for central difference schemes with combustion , 1995 .

[29]  Antony Jameson,et al.  Multigrid solution of the Euler equations using implicit schemes , 1985 .

[30]  Antony Jameson,et al.  Lower-upper implicit schemes with multiple grids for the Euler equations , 1987 .