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Hughes, T. J. R.

Publications and source records attributed to Hughes, T. J. R..

17 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Application of the Galerkin/least-squares formulation to the analysis of hypersonic flows. I - Flow over a two-dimensional ramp

An FEM for the compressible Navier-Stokes equations is introduced. The discretization is based on entropy variables. The methodology is developed within the framework of a Galerkin/least-squares formulation to which a discontinuity-capturing operator is added. Results for three test cases selected among those of the Workshop on Hypersonic Flows for Reentry Problems are presented.

Chalot, F.↗
NASA NTRS1991

Application of the Galerkin/least-squares formulation to the analysis of hypersonic flows. II - Flow past a double ellipse

A finite element method for the compressible Navier-Stokes equations is introduced. The discretization is based on entropy variables. The methodology is developed within the framework of a Galerkin/least-squares formulation to which a discontinuity-capturing operator is added. Results for four test cases selected among those of the Workshop on Hypersonic Flows for Reentry Problems are presented.

Chalot, F.↗
NASA NTRS1990

Symmetrization of conservation laws with entropy for high-temperature hypersonic computations

Results of Hughes, France, and Mallet are generalized to conservation law systems taking into account high-temperature effects. Symmetric forms of different equation sets are derived in terms of entropy variables. First, the case of a general divariant gas is studied; it can be specialized to the usual Navier-Stokes equations, as well as to situations where the gas is vibrationally excited, and undergoes equilibrium chemical reactions. The case of gas in thermochemical nonequilibrium is considered next. Transport phenomena, and in particular mass diffusion, are examined in the framework of symmetric advective-diffusive systems.

Chalot, F.↗
NASA NTRS1989

Compressible flow calculations employing the Galerkin/least-squares method

A multielement group, domain decomposition algorithm is presented for solving linear nonsymmetric systems arising in the finite-element analysis of compressible flows employing the Galerkin/least-squares method. The iterative strategy employed is based on the generalized minimum residual (GMRES) procedure originally proposed by Saad and Shultz. Two levels of preconditioning are investigated. Applications to problems of high-speed compressible flow illustrate the effectiveness of the scheme.

Shakib, F.↗
NASA NTRS1988

The Galerkin/least-squares method for advective-diffusive equations

Galerkin/least-squares finite-element methods are presented for advective-diffusive equations. Galerkin/least-squares represents a conceptual simplification of streamline-upwind Petrov-Galerkin methods, and is in fact applicable to a wide variety of other problem types. A convergence analysis and error estimates are presented. Some numerical results for compressible Navier-Stokes flows are presented.

Hughes, T. J. R.↗
NASA NTRS1986

A Petrov-Galerkin finite element method for the compressible Euler and Navier-Stokes equations

An overview of a new finite element method for the compressible Euler and Navier-Stokes equations is presented. The discretization is based on entropy variables. The method is developed within the framework of a Petrov-Galerkin formulation. Two perturbations are added to the weighting function; one is a generalization of the SUPG operator and the other is designed to enhance shock capturing capability. The treatment of boundary conditions and the consistent calculation of boundary fluxes are addressed. Results of numerical tests are presented which confirm the robustness and wide applicability of the method.

Franca, L. P.↗
NASA NTRS1985

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

Winget, J. M.↗
NASA NTRS1985

Analysis of some fully-discrete algorithms for the one-dimensional heat equation

The present investigation is concerned with a fully discrete accuracy and stability analysis of the one-dimensional heat equation, taking into account the evaluation of two-pass explicit schemes which simultaneously employ lumped and coupled capacity matrices. Schemes of the considered characteristics are not amenable to uncoupled semidiscrete and ordinary differential equation analyses. The obtained results illustrate that superior behavior may be achieved by schemes of the employed type when compared with the performance of the standard one-pass explicit schemes. The key idea in the considered approach is related to the utilization of a reduced-quadrature capacity matrix in the evaluation of the right-hand-side residual.

Hughes, T. J. R.↗
NASA NTRS1985

A high-precision finite element method for shock-tube calculations

A two-pass explicit scheme is developed in order to exploit some of the capabilities of finite difference modeling (FDM) for finite element modeling (FEM), which offers the opportunity to account for any type of geometry in fluid flow modeling. Features of the first-order upwind and the Lax-Wendroff high precision explicit finite difference algorithms are reviewed. A flux limiter is developed for FEM to serve as an analog for the single limiter function which has been defined for the various FDMs. It is shown that an antidiffusive limiter must be introduced into the weighting function which normally multiplies the time-derivative term in the variational equation. The two-pass scheme which results is demonstrated to be the equivalent of FDMs with five-point support. However, the present scheme is valid only for one-dimensional calculations and linear shape functions for shock tube flow phenomena. Further work is required for its use with nonlinear hyperbolic systems.

Hughes, T. J. R.↗
NASA NTRS1985

A one-dimensional shock capturing finite element method and multi-dimensional generalizations

Multi-dimensional generalizations of a one-dimensional finite element shock capturing scheme are proposed. A scalar model problem is used to emphasize that 'preferred directions' are important in multi-dimensional applications. Schemes are developed for the two-dimensional Euler equations. One, based upon characteristics, employs the Mach lines and streamlines as preferred directions.

Hughes, T. J. R.↗
NASA NTRS1984

Augmented weak forms and element-by-element preconditioners: Efficient iterative strategies for structural finite elements. A preliminary study

A weak formulation in structural analysis that provides well conditioned matrices suitable for iterative solutions is presented. A mixed formulation ensures the proper representation of the problem and the constitutive relations are added in a penalized form. The problem is solved by a double conjugate gradient algorithm combined with an element by element approximate factorization procedure. The double conjugate gradient strategy resembles Uzawa's variable-length type algorithms the main difference is the presence of quadratic terms in the mixed variables. In the case of shear deformable beams these terms ensure that the proper finite thickness solution is obtained.

Muller, A.↗
NASA NTRS1984

Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations

A Petrov-Galerkin finite element formulation is presented for first-order hyperbolic systems of conservation laws with particular emphasis on the compressible Euler equations. Applications of the methodology are made to one- and two-dimensional steady and unsteady flows with shocks. Results obtained suggest the potential of the type of methods developed.

Hughes, T. J. R.↗
NASA NTRS1984

Element-by-element Solution Procedures for Nonlinear Structural Analysis

Element-by-element approximate factorization procedures are proposed for solving the large finite element equation systems which arise in nonlinear structural mechanics. Architectural and data base advantages of the present algorithms over traditional direct elimination schemes are noted. Results of calculations suggest considerable potential for the methods described.

Hughes, T. J. R.↗
NASA NTRS1984

Stability and accuracy analysis of some fully-discrete algorithms for the one-dimensional second-order wave equation

The present investigation is concerned with some basic results for a predictor-multicorrector algorithm applied to the one-dimensional wave equation, giving particular attention to so-called 2-pass explicit schemes in which both lumped and coupled mass matrices are employed. In an assessment of the accuracy and stability properties of the algorithms, use is made of the one-dimensional, second-order wave equation. The maximum stable time step of the lumped right-hand-side mass, 2-pass explicit algorithm is twice that of the 1-pass explicit algorithm. Improved accuracy is obtained by employing higher-order, or consistent, right-hand-side, mass.

Hughes, T. J. R.↗
NASA NTRS1984

A shock-capturing finite element method

Finite element methods are developed for a one-dimensional singular perturbation problem involving a nonlinear flux function. In the limit of vanishing dissipation, the numerical flux is found to be almost identical to that due to Engquist and Osher, the only difference being in the treatment of transonic compression. This facilitates sharper resolution of stationary shocks, but is accompanied by loss of smoothness and monotonicity.

Hughes, T. J. R.↗
NASA NTRS1983

Element-by-element factorization algorithms for heat conduction

Element-by-element solution strategies are developed for transient heat conduction problems. Results of numerical tests indicate the effectiveness of the procedures proposed. The small database requirements and attractive architectural features of the algorithms suggest considerable potential for solving large scale problems.

Hughes, T. J. R.↗