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Morgan, K.

Publications and source records attributed to Morgan, K..

50 records · Page 3
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NASA NTRS1987

An adaptive finite element scheme for the Euler and Navier-Stokes equations

The implementation of two explicit finite element schemes for the solution of the compressible Euler and Navier-Stokes equations is presented. The schemes can be employed with general unstructured triangular meshes in two dimensions. Either scheme can therefore be used as the basic solver in a solution adaptive mesh procedure in a direct manner. The particular adaptive approach which is advocated here is intended for the solution of steady state problems only and involves an adaptive regeneration of the grid at prescribed stages during the false transient. The grid regeneration is accomplished by a mesh generator which has the capability of generating triangular grids over computational domains of arbitrary shape. The procedure is illustrated by solving transonic flows over multi-airfoil configurations and high speed flows, involving shock interactions, past circular cylinders.

Morgan, K.↗
NASA NTRS1986

Unstructured multigrid methods for the compressible Euler equations

A two-step explicit finite element based solution procedure for the compressible Euler equations is described. Convergence to steady state can be accelerated by using a multigrid technique. The geometric flexibility of the finite element method is retained by using a sequence of unnested grids. The viability of this approach is demonstrated for elliptic problems and initial experiences with the technique applied to the Euler equations are reported.

Loehner, R.↗
NASA NTRS1986

Convection dominated problems

The paper surveys the last ten years of activity of the INME Swansea, dealing with problems of convection dominated flow. The basic explicit/implicit characteristic Galerkin process and its application to adaptive mesh refinement used in the solution of realistic problems is focused on.

Peraire, J.↗
NASA NTRS1985

An adaptive finite element procedure for compressible high speed flows

A practical finite element-based solution procedure for high-speed inviscid compressible flow problems is described. The method provides time-accurate solutions to the coompressible Euler equations, and is computationally more efficient than the one-step Taylor-Galerkin approach and better suited for implementation on the modern generation of vector computers. The method is coupled to an adaptive mesh refinement process that enables steady state solutions of improved quality to be obtained.

Loehner, R.↗
NASA NTRS1985

Finite element methods for high speed flows

An explicit finite element based solution procedure for solving the equations of compressible viscous high speed flow is presented. The method uses domain splitting to advance the solution with different timesteps on different portions of the mesh. For steady inviscid flows, adaptive mesh refinement procedures are successfully employed to enhance the definition of discontinuities. Preliminary ideas on the application of adaptive mesh refinement to the solution of problems involving steady viscous flow are presented. Sample timings are given for the performance of the finite element code on modern supercomputers.

Loehner, R.↗
NASA NTRS1985

Finite element methods on supercomputers - The scatter-problem

Certain problems arise in connection with the use of supercomputers for the implementation of finite-element methods. These problems are related to the desirability of utilizing the power of the supercomputer as fully as possible for the rapid execution of the required computations, taking into account the gain in speed possible with the aid of pipelining operations. For the finite-element method, the time-consuming operations may be divided into three categories. The first two present no problems, while the third type of operation can be a reason for the inefficient performance of finite-element programs. Two possibilities for overcoming certain difficulties are proposed, giving attention to a scatter-process.

Loehner, R.↗
NASA NTRS1985

High-speed compressible flow and other advection-dominated problems of fluid dynamics

Finite element methods are described for modeling high speed compressible flows with strong advection, problems important to aerodynamics. The situations are characterized by high pressure and temperature gradients, transients and the appearance of discontinuities, factors which require mesh refinement during computations. Techniques are developed for temporal and spatial discretization of a model problem. Several observations are made regarding the explicit and implicit features of the calculations, the use of the Lax-Wendroff scheme to produce a mass-matrix for obtaining accurate results for transients, methods of performing stability analyses, and simplification techniques. Examples are provided of solving the nonlinear shallow-water equations and describing compressible flows, particularly transonic flows. Domain splitting is defined for improving the calculations at each time step and in different parts of the flow regime while simultaneously advancing the calculations towards a solution.

Zienkiewicz, O. C.↗
NASA NTRS1985

Recent developments in FEM-CFD

The current status of CFD with regard to unstructured grids employing finite element methods and Eulerian frames is reviewed. Algorithms suitable for the computation of large three-dimensional problems involving flow past arbitrary geometries are developed. Adaptive mesh refinement strategy is reviewed, and domain splitting or local time-stepping are briefly addressed. The development of search algorithms of optimal order, variable time-stepping Jacobi smoothers for elliptic problems, and transport concepts for hyperbolics to help achieve good performance for unstructured multigrid processes is discussed. As examples, transient supersonic flow in a channel, regular shock reflection of a wall, viscous flow past a protruberance, potential flow past a cylinder, and Burgers equation are considered.

Loehner, R.↗
NASA NTRS1984

The solution of non-linear hyperbolic equation systems by the finite element method

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

Loehner, R.↗
NASA NTRS1984

Adaptive grid refinement for the Euler and compressible Navier-Stokes equations

The incorporation of a simple a posteriori adaptive mesh method into an explicit finite element based procedure for the solution of compressible flow problems is described. The re-interpolation problem is discussed and results are presented that indicate the improvement in solution quality which can be obtained via such an adaptive mesh approach. The method may lead to the appearance of some badly deformed elements which are removed from the domain of computation.

Lohner, R.↗
NASA NTRS1984

High speed inviscid compressible flow by the finite element method

The finite element method and an explicit time stepping algorithm which is based on Taylor-Galerkin schemes with an appropriate artificial viscosity is combined with an automatic mesh refinement process which is designed to produce accurate steady state solutions to problems of inviscid compressible flow in two dimensions. The results of two test problems are included which demonstrate the excellent performance characteristics of the proposed procedures.

Zienkiewicz, O. C.↗
NASA NTRS1982

Finite element analysis of aerodynamic heating in three dimensional viscous high speed compressible flow: An assessment

The current capability of the finite element method for solving problems of viscous flow is reviewed. Much work has been directed to the simulation of incompressible flows and the relevant features are described. The methods available for, and the problems associated with, the finite element solution of high speed viscous compressible flows are analyzed. A plan for developing finite element research in this area with experimental support is presented.

Morgan, K.↗