Large-Eddy Simulation of Shock-Turbulence Interaction

The approximate deconvolution model (ADM) for large-eddy simulation (LES) is adapted for use with a central fourth-order finite volume (Jameson-type) scheme widely applied for aerodynamics calculations of industrial interest. With ADM, an approximation of the unfiltered solution is obtained by repeated filtering, and given a good approximation of the unfiltered solution the nonlinear terms of the filtered Navier‐Stokes equation are computed directly. The effect of scales not represented on the numerical grid is modeled by a relaxation regularization involving a secondary filter operation and a relaxation parameter. The supersonic turbulent boundary layer along a compression ramp at a freestream Mach number of M =3 and a Reynolds number (based on free-stream quantities and the mean momentum thickness at inflow) of Reθ = 1685 is computed to evaluate the ability of ADM to represent discontinuities and turbulent flow regions. It was observed that a unified modeling of discontinuities and turbulence required a local adaptation of the secondary filter used for the relaxation regularization. The LES results are compared with corresponding filtered direct-numerical-simulation (DNS) data. Very good agreement between the filtered DNS and the LES is observed for the mean, fluctuating, and averaged wall quantities.

[1]  Vincent Guinot,et al.  High-Order Fluxes for Conservative Skew-Symmetric-like Schemes in Structured Meshes , 2000 .

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

[3]  Nikolaus A. Adams,et al.  Direct simulation of the turbulent boundary layer along a compression ramp at M = 3 and Reθ = 1685 , 2000, Journal of Fluid Mechanics.

[4]  M. Lesieur,et al.  New Trends in Large-Eddy Simulations of Turbulence , 1996 .

[5]  The Role of Deconvolution and Numerical Discretization in Subgrid-Scale Modeling , 2001 .

[6]  Miguel R. Visbal,et al.  Large-Eddy Simulation of Supersonic Compression-Ramp Flow by High-Order Method , 2001 .

[7]  Nikolaus A. Adams,et al.  Direct and Large-Eddy Simulation of a Transitional Rectangular Jet , 2001 .

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

[9]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[10]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[11]  P. Sagaut.  Large Eddy Simulation for Incompressible Flows , 2001 .

[12]  P. Sagaut,et al.  On the Use of Shock-Capturing Schemes for Large-Eddy Simulation , 1999 .

[13]  Nikolaus A. Adams,et al.  An approximate deconvolution model for large-eddy simulation of compressible flows with finite-volume schemes , 2002 .

[14]  N. Adams,et al.  An approximate deconvolution procedure for large-eddy simulation , 1999 .

[15]  E. Chaput,et al.  RECENT ADVANCES IN AERODYNAMICS INSIDE THE NSMB (NAVIER STOKES MULTI BLOCK) CONSORTIUM , 1998 .

[16]  G. Blaisdell,et al.  Large Eddy Simulation of Compressible Flows , 1996 .

[17]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[18]  T. Taylor,et al.  Computational methods for fluid flow , 1982 .

[19]  Nikolaus A. Adams,et al.  A Subgrid-Scale Deconvolution Approach for Shock Capturing , 2002 .

[20]  Thomas W. Roberts,et al.  The behavior of flux difference splitting schemes near slowly moving shock waves , 1990 .

[21]  P. Lax,et al.  Systems of conservation laws , 1960 .

[22]  Subgrid-Scale Modeling of Turbulent Convection Using Truncated Navier-Stokes Dynamics , 2002 .

[23]  N. Adams,et al.  The approximate deconvolution model for large-eddy simulations of compressible flows and its application to shock-turbulent-boundary-layer interaction , 2001 .

[24]  Large-eddy simulation of complex shear flows using an approximate deconvolution model , 2000 .

[25]  J. P. Boris,et al.  New insights into large eddy simulation , 1992 .

[26]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[27]  Gregory A. Blaisdell,et al.  The effect of the formulation of nonlinear terms on aliasing errors in spectral methods , 1996 .

[28]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[29]  N. Adams,et al.  An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows , 2001 .

[30]  Philip E. Morgan,et al.  An Implicit LES Approach Based on High-order Compact Differencing and Filtering Schemes (Invited) , 2003 .

[31]  David S. Dolling,et al.  Fifty Years of Shock-Wave/Boundary-Layer Interaction Research: What Next? , 2001 .

[32]  G. Sod.  A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws , 1978 .

[33]  A. Bershadskii,et al.  Theory of homogenous turbulence , 1985 .

[34]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[35]  F. Grinstein,et al.  Monotonically integrated large eddy simulation of free shear flows , 1999 .

[36]  P. Sagaut,et al.  Large-eddy simulation of the shock/boundary layer interaction , 2001 .

[37]  F. Grinstein,et al.  Large Eddy simulation of high-Reynolds-number free and wall-bounded flows , 2002 .

[38]  Doyle Knight,et al.  Shock wave boundary layer interactions in high Mach number flows: A critical survey of current CFD prediction capabilities , 1998 .

[39]  S. Stolz,et al.  Large-Eddy Simulation of Separated Flow in a Channel with Streamwise-Periodic Constrictions , 2005 .