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NASA NTRS1991

A new finite element formulation for computational fluid dynamics. X - The compressible Euler and Navier-Stokes equations

A space-time element method is presented for solving the compressible Euler and Navier-Stokes equations. The proposed formulation includes the variational equation, predictor multi-corrector algorithms and boundary conditions. The variational equation is based on the time-discontinuous Galerkin method, in which the physical entropy variables are employed. A least-squares operator and a discontinuity-capturing operator are added, resulting in a high-order accurate and unconditionally stable method. Implicit/explicit predictor multi-corrector algorithms, applicable to steady as well as unsteady problems, are presented; techniques are developed to enhance their efficiency. Implementation of boundary conditions is addressed; in particular, a technique is introduced to satisfy nonlinear essential boundary conditions, and a consistent method is presented to calculate boundary fluxes. Numerical results are presented to demonstrate the performance of the method.

Shakib, Farzin↗

NASA NTRS1993

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Farhat, Charbel↗

NASA NTRS1993

H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows

The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08).

Chang, H. J.↗

NASA NTRS1986

Parabolized Navier-Stokes analysis of ducted turbulent mixing problems with finite-rate chemistry

A hybrid implicit/explicit approach for analyzing 2D ducted turbulent mixing problems with finite-rate chemistry is presented. The approach combines a fully-implicit parabolic mixing algorithm, an explicit viscous-characteristic based shock-capturing algorithm, and linearized implicit chemical kinetic algorithm. The resultant model provides spatial marching solutions of the parabolized Navier-Stokes (PNS) equations for supersonic combustion and viscous nozzle flowfields. Specialized procedures are incorporated to deal with the near wall sublayer and with small central pockets of subsonic flow. A parabolic option is available which can be utilized in the direct or inverse mode for design applications. The ability of the model to treat shock waves and wave/mixing layer interactions is assessed via comparisons of predictions with those of well established explicit shock-capturing Euler (SCIPPY) and PNS (SCIPVIS) models. Applications to a variety of supersonic combustion flowfield problems involving tangential or moderately inclined fuel injection, and, to a viscous nozzle flow problem, are presented. This paper serves to exhibit overall capabilities of the model developed and no comparisons with supersonic combustion data are presented. Such comparisons serve mainly to validate the modeling of the turbulence and turbulence/chemical interactions and will be the subject of a future paper.

Sinha, N.↗

NASA NTRS1985

Implicit/explicit analysis of interactive phenomena in: supersonic, chemically-reacting, mixing and boundary layer problems

An efficient implicit/explicit procedure for solving the parabolized Navier-Stokes (PNS) equations to analyze supersonic, viscous, chemically-reacting flows is presented. The approach combines a fully-implicit algorithm for solving the parabolic mixing/boundary layer equations with an explicit algorithm for determining the hyperbolic pressure field. The unified model, SPLITP, contains provisions for treating bounding/embedded subsonic regions using a pressure-splitting procedure which suppresses elliptic (upstream influence) effects without recourse to sublayer approximations. Several two-equation turbulence models with compressibility and curvature-correction terms are incorporated into SPLITP. Applications to a variety of flow problems are presented which include: ducted supersonic mixing and combustion flowfields, free jets and plumes, and, curved boundary layers and wall jets.

Dash, S. M.↗

NASA NTRS1989

An adaptive implicit/explicit finite element scheme for compressible viscous high speed flow

An adaptive implicit/explicit finite element procedure for the solution of three-dimensional problems of steady compressible viscous high-speed flows is presented. In the vicinity of solid walls, a grid-exhibiting structure in the normal direction is employed, while away from this region the grid is totally unstructured. The implicit form of the algorithm is used near solid walls, with the grid structure being utilized in an equation solution approach based upon line relaxation. The explicit form of the algorithm is used elsewhere. Grid adaptation is achieved by means of adaptive remeshing. To illustrate the performance of the proposed method, solutions are obtained for the problems of shock-boundary layer interaction and shock-shock interaction on a swept cylindrical leading edge. Comparisons are made with experimental observations.

Hassan, O.↗

NASA NTRS1989

The simulation of 2D compressible viscous high speed flow by the finite element method

Am implicit/explicit procedure for the solution of problems of two-dimensional steady compressible viscous high-speed flows is presented. In the vicinity of solid walls, a grid which need only exhibit structure in the normal direction is employed while, away from this region, the grid is totally unstructured. The implicit form of the algorithm is used near solid walls, with the grid structure being utilized in an equation solution approach, based upon line relaxation. The explicit form of the algorithm is used elsewhere. Grid adaptation is achieved by means of adaptive remeshing. To illustrate the performance of the proposed method, problems of shock-boundary layer interaction and flow over a simulated forebody at high Mach number are included.

Hassan, O.↗

NASA NTRS1993

Line relaxation methods for the solution of 2D and 3D compressible flows

An implicit finite element based algorithm for the compressible Navier-Stokes equations is outlined, and the solution of the resulting equation by a line relaxation on general meshes of triangles or tetrahedra is described. The problem of generating and adapting unstructured meshes for viscous flows is reexamined, and an approach for both 2D and 3D simulations is proposed. An efficient approach appears to be the use of an implicit/explicit procedure, with the implicit treatment being restricted to those regions of the mesh where viscous effects are known to be dominant. Numerical examples demonstrating the computational performance of the proposed techniques are given.

Hassan, O.↗