Computation of three-dimensional, inviscid supersonic flows

The paper sets forth in detail a method for the finite-difference computation of three-dimensional supersonic fields in an Eulerian mesh. First-, second-, and third-order finite difference schemes are examined. Attention is given to proper treatment of the impermeable and permeable boundaries encompassing the computational plane. Numerical results are presented for certain specific configurations: a conical wing-body combination, internal corner flow, a two-dimensional blunt body, an interfering shock problem, and three-dimensional inviscid supersonic flow past a shuttle-orbiter type vehicle.

[1]  F. Marconi,et al.  Computation of Three Dimentional Flows about aircraft configurations , 1973 .

[2]  Paul Kutler,et al.  Multishocked, Three-Dimensional Supersonic Flowfields with Real Gas Effects , 1973 .

[3]  L. R. Fowell Exact and Approximate Solutions for the Supersonic Delta Wing , 1956 .

[4]  Paul Kutler,et al.  Application of selected finite difference techniques to the solution of conical flow problems , 1969 .

[5]  P. Lax,et al.  Difference schemes for hyperbolic equations with high order of accuracy , 1964 .

[6]  Mamoru Inouye,et al.  Time-Split Finite-Volume Method for Three-Dimensional Blunt-Body Flow , 1973 .

[7]  L. Redekopp,et al.  Supersonic interference flow along the corner of intersecting wedges , 1966 .

[8]  P. Roache,et al.  Nonuniform mesh systems , 1971 .

[9]  S. Powers,et al.  A method for determining the complete flow field around conical wings at supersonic/ hypersonic speeds. , 1969 .

[10]  Michael Abbett BOUNDARY CONDITION CALCULATION PROCEDURES FOR INVISCID SUPERSONIC FLOW FIELDS , 1973 .

[11]  The computation of supersonic flow fields about wing-body combinations by “shock-capturing” finite difference techniques , 1971 .

[12]  Gino Moretti,et al.  Importance of Boundary Conditions in the Numerical Treatment of Hyperbolic Equations , 1969 .

[13]  R. D. Richtmyer,et al.  Difference methods for initial-value problems , 1959 .

[14]  John V. Rakich,et al.  Calculation of Hypersonic Flow over Bodies of Revolution at Small Angles of Attack , 1965 .

[15]  D. Babayev Numerical solution of the problem of flow round the upper surface of a triangular wing by a supersonic stream , 1963 .

[16]  I. Bohachevsky,et al.  Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics , 1959 .

[17]  R. F. Warming,et al.  The modified equation approach to the stability and accuracy analysis of finite-difference methods , 1974 .

[18]  A. P. Bazzhin Some results of calculations of flows around conical bodies at large incidence angles , 1971 .

[19]  P. Kutler Numerical solution for the inviscid supersonic flow in the corner formed by two intersecting wedges. , 1973 .

[20]  On the shock-on-shock interaction problem , 1974 .

[21]  E. Hopf The partial differential equation ut + uux = μxx , 1950 .

[22]  Ronald F. Probstein,et al.  Hypersonic Flow Theory , 1959 .

[23]  Paul Kutler,et al.  Shock-Capturing, Finite-Difference Approach to Supersonic Flows , 1971 .

[24]  P. Kutler,et al.  Comparison of characteristics and shock capturing methods with application to the space shuttle vehicle. , 1972 .

[25]  Paul Kutler Supersonic Flow in the Corner Formed by Two Intersecting Wedges , 1974 .

[26]  Robert E. Mates,et al.  A direct method for calculation of the flow about an axisymmetric blunt body at angle of attack. , 1966 .

[27]  Paul Kutler,et al.  Second- and Third-Order Noncentered Difference Schemes for Nonlinear Hyperbolic Equations , 1973 .

[28]  D. A. Babaev,et al.  NUMERICAL SOLUTION OF THE PROBLEM OF SUPERSONIC FLOW PAST THE LOWER SURFACE OF A DELTA WING , 1963 .

[29]  P. Lax Weak solutions of nonlinear hyperbolic equations and their numerical computation , 1954 .

[30]  G. Moretti,et al.  A time-dependent computational method for blunt body flows. , 1966 .

[31]  C. W. Hirt Heuristic stability theory for finite-difference equations☆ , 1968 .

[32]  David L. Merritt,et al.  WIND TUNNEL SIMULATION OF HEAD-ON BOW WAVE-BLAST WAVE INTERACTIONS, , 1967 .

[33]  Paul Kutler,et al.  Computation of Space Shuttle Flowfields Using Noncentered Finite-Difference Schemes , 1973 .

[34]  K Oswatitsch,et al.  The Wave Formation and Sonic Boom Due to a Delta Wing , 1972 .

[35]  Robert W. MacCormack,et al.  A generalized hyperbolic marching technique for three-dimensional supersonic flow with shocks , 1975 .

[36]  S. Z. Burstein,et al.  Numerical methods in multidimensional shocked flows , 1964 .

[37]  P. D. Thomas,et al.  Numerical Solution for Three-Dimensional Inviscid Supersonic Flow , 1972 .

[38]  M. Abbett Boundary condition computational procedures for inviscid, supersonic steady flow field calculations , 1971 .

[39]  Peter Henrici,et al.  Constructive aspects of the fundamental theorem of algebra : proceedings of a symposium conducted at the IBM Research Laboratory, Zürich-Rüschlikon, Switzerland, June 5-7, 1967 , 1972 .

[40]  J. Gary On certain finite difference schemes for hyperbolic systems , 1964 .

[41]  I. Bohachevsky,et al.  A direct method for computation of nonequilibrium flows with detached shock waves. , 1965 .

[42]  J. E. West,et al.  Interaction of the Corner of Intersecting Wedges at a Mach Numer of 3 and High Reynolds Numbers. , 1971 .

[43]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[44]  R. Maccormack The Effect of Viscosity in Hypervelocity Impact Cratering , 1969 .

[45]  G. Moretti,et al.  A complete numerical technique for the calculation of three-dimensional inviscid supersonic flows , 1972 .

[46]  R. Maccormack,et al.  Survey of computational methods for three-dimensional supersonic inviscid flows with shocks , 1973 .

[47]  P. Kutler,et al.  Application of shock capturing and characteristics methods to shuttle flow fields , 1972 .

[48]  E. Hopf,et al.  The Partial Differential Equation u_i + uu_x = μu_t , 1950 .

[49]  V. Rusanov,et al.  On difference schemes of third order accuracy for nonlinear hyperbolic systems , 1970 .

[50]  C. Nebbeling,et al.  Investigation of the Expansion Side of a Delta Wing at Supersonic Speed , 1973 .

[51]  Eugenia Kálnay de Rivas On the use of nonuniform grids in finite-difference equations , 1972 .

[52]  T. Teichmann,et al.  Introduction to physical gas dynamics , 1965 .