A hybrid explicit-implicit numerical algorithm for the three-dimensional compressible Navier-Stokes equations

A hybrid explicit-implicit numerical algorithm has been developed for the three-dimensional mean compressible Navier-Stokes equations. The algorithm combines the explicit finite difference algorithm of MacCormack and an implicit algorithm for the viscous sublayer and transition wall regions of the turbulent boundary layers. The algebraic turbulent eddy-viscosity model of Baldwin and Lomax is employed. A bodyoriented coordinate transformation is utilized to facilitate treatment of arbitrary flow regions. The hybrid algorithm has been vectorized on the CDC CYBER 203 computer using the SL/1 vector programming language developed at NASA Langley. The accuracy of the numerical algorithm, established previously for twodimensional flows with strong viscous-inviscid interaction (including flow separation), is validated for threedimensional flows. The algorithm is applied to the interaction of an oblique shock wave with a turbulent boundary layer in three dimensions. The computed results generally are found to be in close agreement with the experimental data. The hybrid algorithm is shown to provide a substantial improvement in computational efficiency compared to a vectorized MacCormack explicit algorithm alone.

[1]  R. Swanson.  Navier-Stokes solutions for nonaxisymmetric nozzle flows , 1981 .

[2]  D. Knight.  Improved Calculation of High Speed Inlet Flows. Part II: Results , 1981 .

[3]  B. Oskam,et al.  Mach 3 oblique shock wave/turbulent boundary layer interactions in three dimensions , 1976 .

[4]  Gary S. Settles,et al.  Investigation of Three-Dimensional Shock/Boundary-Layer Interactions at Swept Compression Corners , 1980 .

[5]  B. Oskam,et al.  Oblique Shock Wave/Turbulent Boundary Layer Interactions in Three Dimensions at Mach 3. Part II. , 1978 .

[6]  D. S. Dolling,et al.  Upstream influence in sharp fin-induced shock wave turbulent boundary-layer interaction , 1981 .

[7]  E. Hopkins,et al.  An evaluation of theories for predicting turbulent skin friction and heat transfer on flat plates at supersonic and hypersonic Mach numbers , 1971 .

[8]  Evaluation of the Baldwin-Lomax turbulence model for two-dimensionalshock wave boundary layer interactions , 1983 .

[9]  Ajay Kumar,et al.  Three-dimensional inviscid analysis of the scramjet inlet flow field , 1982 .

[10]  Robert W. MacCormack,et al.  Numerical solution of the interaction of a shock wave with a laminar boundary layer , 1971 .

[11]  John L. Stollery,et al.  An experimental study of the interaction between a glancing shock wave and a turbulent boundary layer , 2005 .

[12]  M. Childs,et al.  Wall-wake velocity profile for compressible nonadiabatic flows , 1976 .

[13]  Doyle D Knight,et al.  Calculation of high-speed inlet flows using the Navier-Stokes equations. , 1980 .

[14]  Joe F. Thompson,et al.  Boundary-fitted coordinate systems for numerical solution of partial differential equations—A review , 1982 .

[15]  D. Dolling,et al.  An examination of blunt fin-induced shock wave turbulent boundary layer interactions , 1979 .

[16]  Gary S. Settles,et al.  Scaling of Two- and Three-Dimensional Shock/Turbulent Boundary-Layer Interactions at Compression Corners , 1982 .

[17]  Louis Rosenhead,et al.  Laminar boundary layers , 1963 .

[18]  S. Rubin.  Incompressible flow along a corner , 1966, Journal of Fluid Mechanics.

[19]  C. Law.  Three-Dimensional Shock Wave-Turbulent Boundary Layer Interactions at Mach 6 , 1975 .

[20]  R. Maccormack,et al.  A numerical method for solving the Navier-Stokes equations with application to shock-boundary layer interactions , 1975 .

[21]  Impingement of an oblique shock wave on a cylinder , 1983 .

[22]  R. F. Warming,et al.  An Implicit Factored Scheme for the Compressible Navier-Stokes Equations , 1977 .

[23]  L. B. Schiff,et al.  Computation of supersonic viscous flows around pointed bodies at large incidence , 1983 .

[24]  H. Lomax,et al.  Thin-layer approximation and algebraic model for separated turbulent flows , 1978 .

[25]  H. Keller.  Accurate Difference Methods for Nonlinear Two-Point Boundary Value Problems , 1974 .

[26]  W. L. Hankey,et al.  Three-Dimensional Supersonic Interacting Turbulent Flow along a Corner , 1978 .

[27]  Tuncer Cebec,et al.  Calculation of Compressible Turbulent Boundary Layers with Heat and Mass Transfer , 1971 .

[28]  J S Shang,et al.  The Performance of a Vectorized 3-D Navier-Stokes Code on the CRAY-1 Computer. , 1979 .

[29]  D. Knight.  Improved Calculation of High Speed Inlet Flows: Part I. Numerical Algorithm , 1981 .

[30]  J. Steger,et al.  Implicit Finite-Difference Simulations of Three-Dimensional Compressible Flow , 1980 .

[31]  Computation of Supersonic Turbulent Flows over an Inclined Ogive-Cylinder-Flare , 1981 .

[32]  J. J. Lambiotte.  Effect of virtual memory on efficient solution of two model problems , 1977 .

[33]  R. Maccormack,et al.  Numerical solution of a three-dimensional shock wave and turbulent boundary-layer interaction , 1978 .

[34]  D. J. Peake.  Three-dimensional swept shock/turbulent boundary-layer separations with control by air injection , 1976 .

[35]  P. G. Buning,et al.  Performance of a Vectorized Three-Dimensional Navier-Stokes Code on the CRAY-1 Computer , 1980 .