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Maccormack, R. W.

Publications and source records attributed to Maccormack, R. W..

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

An efficient explicit-implicit-characteristic method for solving the compressible Navier-Stokes equations

Explicit, implicit, and characteristic finite-difference methods are applied to solve model equations representative of the compressible Navier-Stokes equations. An approach is then formulated for solving the Navier-Stokes equation at high Reynolds numbers. The approach has drastically reduced the computation time required to obtain viscous flow solutions. Computational results for shock wave separated flows are presented.

Maccormack, R. W.↗
NASA NTRS1977

Numerical solution of supersonic laminar flow over a three-dimensional compression corner

A newly developed, rapid numerical scheme is extended to three dimensions to solve the complete Navier-Stokes equations for a supersonic, laminar flow over a compression corner with sidewall effects. The program is coded so that it can solve for a general curved ramp surface geometry such as found in inlets and fuselage-wing-flap junctions. A test case of Mach 3.0 flow is calculated. In regions where three-dimensional effects are small, good agreement is obtained between the present calculation and previous two-dimensional solutions. In other regions, the results show complex three-dimensional flow-field interactions including shock-shock and shock/boundary-layer interactions

Hung, C. M.↗
NASA NTRS1976

Modifications of the law of the wall and algebraic turbulence modelling for separated boundary layers

Various modifications of the conventional algebraic eddy viscosity turbulence model are investigated for application to separated flows. Friction velocity is defined in a way that avoids singular behavior at separation and reattachment but reverts to the conventional definition for flows with small pressure gradients. This leads to a modified law of the wall for separated flows. The effect on the calculated flow field of changes in the model that affect the eddy viscosity at various distances from the wall are determined by (1) switching from Prandtl's form to an inner layer formula due to Clauser at various distances from the wall, (2) varying the constant in the Van Driest damping factor, (3) using Clauser's inner layer formula all the way to the wall, and (4) applying a relaxation procedure in the evaluation of the constant in Clauser's inner layer formula. Numerical solutions of the compressible Navier-Stokes equations are used to determine the effects of the modifications. Experimental results from shock-induced separated flows at Mach numbers 2.93 and 8.45 are used for comparison. For these cases improved predictions of wall pressure distribution and positions of separation and reattachment are obtained from the relaxation version of the Clauser inner layer eddy viscosity formula.

Baldwin, B. S.↗
NASA NTRS1976

Numerical simulation of supersonic and hypersonic turbulent compression corner flows using relaxation models

Relaxation turbulence eddy viscosity models are incorporated to solve the complete Navier-Stokes equations for supersonic and hypersonic flows over a two-dimensional compression corner. The system of equations is solved by a time-split, second-order accurate numerical scheme. Details of relaxation process are studied, and several relaxation models are tested and compared. Good improvement in the prediction of upstream pressure propagation is obtained for a Mach number of 2.96, and Reynolds number of 10,000,000, with wedge angle of 25 deg. However, the application of the relaxation models to hypersonic flow at Mach number 8.66 and Reynolds number of 22,000,000, with highly cooled wall, shows unfavorable effects on heat transfer and skin friction in the reattachment and recompression regions.

Hung, C. M.↗
NASA NTRS1976

Analytic numerical solutions for shock waves

Study of weak solutions of simple wave equation, inviscid Burgers equation, and Euler equations has resulted in technique for accurate prediction of shock waves occurring in inviscid supersonic flows.

Maccormack, R. W.↗
NASA NTRS1976

Steady supersonic flowfields with embedded subsonic regions

Supersonic flow past a blunt body is considered, where the flow contains an embedded subsonic region which lies between the shock wave and the body surface and is bounded by sonic lines from the body to the shock. A numerical approach is taken, which uses a basic finite difference scheme that solves the unsteady fluid dynamic equations in integral form. The unsteady equations are everywhere hyperbolic in time so no distinction need be made between subsonic and supersonic regions. Solutions to the mixed elliptic and hyperbolic steady flow equations are approached asymptotically in time. The method is illustrated for two-dimensional flows.

Maccormack, R. W.↗
NASA NTRS1976

Fluid dynamics applications of the Illiac IV computer

The Illiac IV is a parallel-structure computer with computing power an order of magnitude greater than that of conventional computers. It can be used for experimental tasks in fluid dynamics which can be simulated more economically, for simulating flows that cannot be studied by experiment, and for combining computer and experimental simulations. The architecture of Illiac IV is described, and the use of its parallel operation is demonstrated on the example of its solution of the one-dimensional wave equation. For fluid dynamics problems, a special FORTRAN-like vector programming language was devised, called CFD language. Two applications are described in detail: (1) the determination of the flowfield around the space shuttle, and (2) the computation of transonic turbulent separated flow past a thick biconvex airfoil.

Maccormack, R. W.↗
NASA NTRS1976

A rapid solver for hyperbolic systems of equations

A numerical method is proposed for solving the time-dependent compressible Navier-Stokes equations in two dimensions. The equations are time-split into a hyperbolic part and a parabolic part. This paper describes an explicit numerical method for solving the hyperbolic (inviscid) part. The hyperbolic operator is explicit, conservative, uses characteristic relations to predict convection and pressure fields, and is stable under a specified condition.

Maccormack, R. W.↗
NASA NTRS1976

An efficient numerical method for solving the time-dependent compressible Navier-Stokes equations at high Reynolds number

A fine-mesh method incorporating two new operators, which drastically reduces the computation time, has been developed for solving the time-dependent Navier-Stokes equations at flight Reynolds numbers. The approach time-splits the equations into a hyperbolic part and a parabolic part, solves the hyperbolic part by a new explicit numerical method based on characteristics theory, and solves the parabolic part by a new efficient implicit parabolic method. The method has reduced the computation time by one and two orders of magnitude from that required previously to solve for the interaction of a shock wave with a boundary layer on a flat plate.

Maccormack, R. W.↗
NASA NTRS1975

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

Baldwin, B. S.↗
NASA NTRS1975

A numerical method for solving the Navier-Stokes equations with application to shock-boundary layer interactions

A numerical method for solving the compressible form of the unsteady Navier-Stokes equations is described. This method was originally presented in 1970 and has since been modified during the development of computer programs at Ames for implementing models that account for the effects of turbulence in shock-induced separated flows. Although this paper does not describe the turbulence models themselves, a complete description of the basic numerical method is given with emphasis on the choice of a computational mesh for high Reynolds number flows, finite-difference approximations for mixed partial derivatives, extension of the Courant-Friedrichs-Lewy stability condition for viscous flows, mesh boundary conditions, and numerical smoothing for strong shock-wave calculations.

Maccormack, R. W.↗
NASA NTRS1975

Numerical solutions of supersonic and hypersonic laminar flows over a two-dimensional compression corner

An efficient time-splitting, second-order accurate, numerical scheme is used to solve the complete Navier-Stokes equations for supersonic and hypersonic laminar flow over a two-dimensional compression corner. A fine, exponentially stretched mesh spacing is used in the region near the wall for resolving the viscous layer. Good agreement is obtained between the present computed results and experimental measurement for a Mach number of 14.1, a Reynolds number of 104,000, and wedge angles of 15, 18, and 24 deg. The details of the pressure variation across the boundary layer are given, and a correlation between the leading edge shock and the peaks in surface pressure and heat transfer is observed.

Hung, C. M.↗
NASA NTRS1975

Interaction of strong shock wave with turbulent boundary layer

The reported investigation represents an extension of the time-dependent solution of separated laminar flows based on the complete Navier-Stokes equations reported by MacCormack (1971) and Carter (1973). The current study includes turbulence models in conjunction with the compressible flow equations. The calculations start with a uniform flow except for values imposed along the upstream and outer boundaries. The basic numerical method is discussed along with questions concerning the exponential accuracy and the resolution of the viscous sublayer in a compressed region.

Baldwin, B. S.↗
NASA NTRS1975

A generalized hyperbolic marching technique for three-dimensional supersonic flow with shocks

The current paper introduces a generalized, nonorthogonal coordinate system for application to supersonic flows with such large angles between streamlines of the initial Cauchy data and the marching direction that the velocity component in the marching direction is actually subsonic. Finite-difference operators are developed to solve the three-dimensional, steady, inviscid conservation equations of fluid flow referenced to this general frame. Moreover, a new method of aligning the difference mesh to the bow shock wave is presented which eliminates both the necessity for differencing the free-stream flow properties and the spurious fluctuations that often arise in conservative variables when they are differenced across the discontinuity. Results are given for the case of flow past a conical surface.

Rizzi, A. W.↗
NASA NTRS1974

The influence of the computational mesh on accuracy for initial value problems with discontinuous or nonunique solutions

Discontinuous, or weak, solutions of the wave equation, the inviscid form of Burgers equation, and the time-dependent, two-dimensional Euler equations are studied. A numerical method of second-order accuracy in two forms, differential and integral, is used to calculate the weak solutions of these equations for several initial value problems, including supersonic flow past a wedge, a double symmetric wedge, and a sphere. The effect of the computational mesh on the accuracy of computed weak solutions including shock waves and expansion phenomena is studied. Modifications to the finite-difference method are presented which aid in obtaining desired solutions for initial value problems in which the solutions are nonunique.

Maccormack, R. W.↗
NASA NTRS1974

Numerical solution of the time-dependent compressible Navier-Stokes equations in inlet regions

The results of a study to determine the effects of compressibility on the viscous flow through channels that have straight, parallel walls are presented. Two channel configurations are considered, the flow between two semi-infinite flat plates with uniform flow prescribed at the inlet plane and a cascade of semi-infinite flat plates with uniform flow introduced upstream. The flow field is modeled by using the time dependent, compressible Navier-Stokes equations. Time dependent solutions are obtained by using an explicit finite difference technique which advances the pressure on near field subsonic boundaries such that accurate steady state solutions are obtained. Steady state results at Reynolds number 20 and 150 are presented for Mach numbers between 0.09 and 0.36 and compared with the incompressible solutions of previous studies.

Olson, L. E.↗