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Lomax, H.

Publications and source records attributed to Lomax, H..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

An optimized finite-difference scheme for wave propagation problems

Two fully-discrete finite-difference schemes for wave propagation problems are presented, a maximum-order scheme and an optimized (or spectral-like) scheme. Both combine a seven-point spatial operator and an explicit six-stage time-march method. The maximum-order operator is fifth-order in space and is sixth-order in time for a linear problem with periodic boundary conditions. The phase and amplitude errors of the schemes obtained using Fourier analysis are given and compared with a second-order and a fourth-order method. Numerical experiments are presented which demonstrate the usefulness of the schemes for a range of problems. For some problems, the optimized scheme leads to a reduction in global error compared to the maximum-order scheme with no additional computational expense.

Zingg, D. W.↗
NASA NTRS1993

Some aspects of high-order numerical solutions of the linear convection equation with forced boundary conditions

A six-stage low-storage Runge-Kutta time-marching method is presented and shown to be an efficient method for use with high-accuracy spatial difference operators for wave propagation problems. The accuracy of the method for inhomogeneous ordinary differential equations is demonstrated through numerical solutions of the linear convection equation with forced boundary conditions. Numerical experiments are presented simulating a sine wave and a Gaussian pulse propagating into and through the domain. For practical levels of mesh refinement corresponding to roughly ten points per wavelength, the six-stage Runge-Kutta method is more accurate than the popular fourth-order Runge-Kutta method. Further numerical experiments are presented which show that the numerical boundary scheme at an inflow boundary can be a significant source of error when high-accuracy spatial discretizations are used.

Zingg, D. W.↗
NASA NTRS1986

A new approximate LU factorization scheme for the Reynolds-averaged Navier-Stokes equations

A new approximate LU factorization scheme is developed to solve the steady state Reynolds-averaged Navier-Stokes (NS) equations. Central differencing is used for both implicit and explicit operator and special care is taken to obtain well-conditioned factors on the implicit side. The scheme is then analyzed and optimized according to a simple linear analysis. It is unconditionally stable for the model hyperbolic equation in both two- and three-dimensions. However, the requirement for well-conditioned factors has essentially limited the effective time step the scheme can achieve. Supersonic and transonic three-dimensinal flows past a hemisphere cylinder are computed to demonstrate the convergence characteristics of the scheme. A good convergence rate is achieved for the inviscid case. Finally, an explicit eigenvector annihilation procedure is adopted successfully to remove the stiffness caused by the fine grid spacing for viscous flows.

Pan, D.↗
NASA NTRS1986

A numerical study of shock wave diffraction by a circular cylinder

The nonstationary shock wave diffraction patterns generated by a blast wave impinging on a circular cylinder are numerically simulated using a second-order hybrid upwind method for solving the two-dimensional inviscid compressible Euler equations of gasdynamics. The complete diffraction patterns, including the transition from regular to Mach reflection, trajectory of the Mach triple point and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the cylinder are reported in detail. Pressure-time history and various contour plots are also included. Comparison between the work of Bryson and Gross (1961) which included both experimental schlieren pictures and theoretical calculations using Whitham's ray-shock theory and results of the present finite difference computation indicate good agreement in every aspect except for some nonideal gas and viscous effects which are not accounted for by the Euler equations.

Yang, J.-Y.↗
NASA NTRS1984

Some physical and numerical aspects of computing the effects of viscosity on fluid flow

Some physical, analytical, and computational aspects of viscous flow are examined with reference to examples of computed flows. The discussion of the physical aspects covers the development of important scales used to reference flow phenomena in laminar and turbulent shear layers; the usefulness of the concepts of circulation and vorticity; and some relatively large-scale organized structures that have recently been identified in transitional and fully developed turbulent flows. Among the analytical aspects discussed are a compact presentation of the compressible Navier-Stokes equations, the Reynolds-averaged form of these equations, and a simplified description of some forms of turbulent models. Finally, results of a simulation of the onset of transition, direct turbulence simulations, and large-eddy simulations are given.

Lomax, H.↗
NASA NTRS1983

A nonstationary relaxation method for the Cauchy-Riemann and 1-D Euler equations

The Cauchy-Riemann equations and the 1-D Euler equations are expressed in generalized coordinates and then cast in finite difference form by using central differencing throughout. The resulting matrix representation has an eigensystem that permits the development of an annihilation process using complex arithmetic in a block tridiagonal solver. Initial numerical experiments show that the process has potential for use as a relaxation procedure for the Euler equations.

Liu, Y.↗
NASA NTRS1982

Reynolds averaged Navier-Stokes computations of transonic flows The-state-of-the-art

The state of the art in computer simulations for transonic flowfields requiring solutions for the Navier-Stokes equations is assessed. It is noted that current simulations of transonic flowfields require comparisons with experimental results because the simulations are not free from discretization errors. Cases of turbulence are treated with weighted variables in a time-averaged scheme to yield Reynolds averaged Navier-Stokes equations. The turbulence is modeled in a first-order approach with a Reynolds stress tensor or a second-order approach where the tensor is obtained from the Navier-Stokes equations. The choice of coordinate systems and dependent variables for simulating the flow around airfoils is discussed, with particular attention to curvilinear coordinates. The determinations of boundary conditions is examined, along with numerical methods related to physical phenomena

Mehta, U.↗
NASA NTRS1981

Some prospects for the future of computational fluid dynamics

For the oncoming decade it is anticipated that new generations of high-capacity and high-speed computers will appear and that some of them will be dedicated to fluid dynamics applications. An attempt is made here to examine the potential for a new generation of numerical techniques that will accompany the computer advances. Possibilities for improvement in solution techniques, grid adaptations, turbulence approximations, language constructions, and general code robustness are considered.

Lomax, H.↗
NASA NTRS1979

Simulation of three-dimensional compressible viscous flow on the Illiac IV computer

Complicated three-dimensional viscous transonic flows about bodies at high angles of attack are solved on the Illiac IV computer. It is shown that certain approximate forms of the compressible Reynolds-averaged Navier-Stokes equations can be computed about realistic three-dimensional geometries with relative ease on the Illiac IV. The ease and efficiency with which this can be done depend on the approximations made in the basic equations, the choice of the numerical algorithm used for the solution, and the data-base system that controls the data management and identifies and manipulates the vectors. A pencil data-base system is found to be particularly suitable for the approximations and numerical method chosen to produce the results presented. In addition, some comparisons are made of computer predictions with experimental results for various lows about hemisphere-cylinders in both subsonic and supersonic free streams. The same viscous model and numerical model are used, showing good qualitative agreement in the location of separation lines and pressure distributions.

Pulliam, T. H.↗
NASA NTRS1979

Numerical solution of compressible viscous flows

The presented review is concerned with the problem of calculating compressible viscous flows. Basic numerical considerations and problems associated with calculating viscous flows are examined and current numerical approaches toward the solution of the Navier-Stokes equations are discussed. It is pointed out that the numerical solution of the full time-dependent equations for turbulent flow is not practical with present computers. Therefore, turbulence effects must be accounted for by modeling. Developments related to turbulence modeling are described. In connection with a discussion of numerical methods for solving viscous flow equations, attention is given to numerical domains of dependence of typical explicit and implicit methods, the diffusion problem, the convection-diffusion problem, and the split-hybrid method.

Maccormack, R. W.↗
NASA NTRS1978

Three-dimensional computational aerodynamics in the 1980's

The future requirements for constructing codes that can be used to compute three-dimensional flows about aerodynamic shapes should be assessed in light of the constraints imposed by future computer architectures and the reality of usable algorithms that can provide practical three-dimensional simulations. On the hardware side, vector processing is inevitable in order to meet the CPU speeds required. To cope with three-dimensional geometries, massive data bases with fetch/store conflicts and transposition problems are inevitable. On the software side, codes must be prepared that: (1) can be adapted to complex geometries, (2) can (at the very least) predict the location of laminar and turbulent boundary layer separation, and (3) will converge rapidly to sufficiently accurate solutions.

Lomax, H.↗
NASA NTRS1978

Thin-layer approximation and algebraic model for separated turbulent flows

An algebraic turbulence model for two- and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer. Properties of the model are determined and comparisons made with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil. Separation and reattachment points from numerical Navier-Stokes solutions agree with experiment within one boundary-layer thickness. Use of law-of-the-wall boundary conditions does not alter the predictions significantly. Applications of the model to other cases are contained in companion papers.

Baldwin, B.↗
NASA NTRS1977

Variants and extensions of a fast direct numerical cauchy-riemann solver, with illustrative applications

Revised and extended versions of a fast, direct (noniterative) numerical Cauchy-Riemann solver are presented for solving finite difference approximations of first order systems of partial differential equations. Although the difference operators treated are linear and elliptic, one significant application of these extended direct Cauchy-Riemann solvers is in the fast, semidirect (iterative) solution of fluid dynamic problems governed by the nonlinear mixed elliptic-hyperbolic equations of transonic flow. Different versions of the algorithms are derived and the corresponding FORTRAN computer programs for a simple example problem are described and listed. The algorithms are demonstrated to be efficient and accurate.

Martin, E. D.↗
NASA NTRS1976

Turbulence and numerical wind tunnels

The feasibility and possible significance of aerodynamic simulations are considered. Despite certain limitations, there is reason to believe that many useful and important flows containing turbulence can be computed with an accuracy acceptable for use in aircraft designs. Attention is given to the equations for unsteady fluid flow, the direct calculation of unsteady viscous flows, the direct calculation of nonlinear equations, the computation of flows about bodies using turbulence modeling, future developments in numerical methods, and future developments in computers.

Lomax, H.↗
NASA NTRS1975

Relaxation methods in fluid mechanics

The present work considers the iterative solution of a coupled set of difference equations and examines methods that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. Methods are studied with regard to their efficiency and economy of computer resources. The basic principles of classical relaxation are set forth, with attention confined to linear elliptic equations. This discussion involves the evaluation of the spectral radius that is the magnitude of the eigenvalue with largest modulus. The subject of relaxation is then related to the study of ordinary differential equations and hyperbolic partial differential equations. Problems that occur when linearly dependent eigenvectors appear in the relaxation matrix are discussed, leading to multiply connected eigenvalues in the Jordan canonical form. Finally, a brief survey of relaxation methods used in aerodynamics is given.

Lomax, H.↗
NASA NTRS1975

Recent progress in numerical techniques for flow simulation

Recent developments in the use of numerical methods for fluid flow simulation show an increasing tendency to use numerical operators that can, in various ways, be factored. Use of methods having this property often increases the accuracy and efficiency of computer codes. Tracing the factorization property provides a unity to the basic concepts involved in the development of cyclic reduction, predictor-corrector, splitting, fast Fourier transform, and pseudospectral methods.-

Lomax, H.↗
NASA NTRS1975

The numerical simulation of low frequency unsteady transonic flow fields

The lowest order approximation to the Euler equations for unsteady, transonic flow about a thin airfoil is considered and a semiimplicit difference scheme is applied to a simplified governing equation which is a suitable modification of this approximation for low-frequency motion. In another approach the approximation first considered is retained as the governing equation and a semiimplicit difference scheme is employed. The computed results obtained in both cases are discussed.

Ballhaus, W. F.↗