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  • 1
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    Parallel, adaptive finite element methods for conservation laws (1994)
    In:  Other Sources
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    Publication Date: 2011-08-24
    Description: We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: Applied Numerical Mathematics (ISSN 0618-9274); p. 255-283
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  • 2
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    Dynamic mesh adaption for triangular and tetrahedral grids (1993)
    In:  CASI
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    Publication Date: 2013-08-31
    Description: The following topics are discussed: requirements for dynamic mesh adaption; linked-list data structure; edge-based data structure; adaptive-grid data structure; three types of element subdivision; mesh refinement; mesh coarsening; additional constraints for coarsening; anisotropic error indicator for edges; unstructured-grid Euler solver; inviscid 3-D wing; and mesh quality for solution-adaptive grids. The discussion is presented in viewgraph form.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: NASA. Langley Research Center, Unstructured Grid Generation Techniques and Software; p 181-192
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  • 3
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    An adaptive mesh-moving and refinement procedure for one-dimensional conservation laws (1993)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: We examine the performance of an adaptive mesh-moving and /or local mesh refinement procedure for the finite difference solution of one-dimensional hyperbolic systems of conservation laws. Adaptive motion of a base mesh is designed to isolate spatially distinct phenomena, and recursive local refinement of the time step and cells of the stationary or moving base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. These adaptive procedures are incorporated into a computer code that includes a MacCormack finite difference scheme wih Davis' artificial viscosity model and a discretization error estimate based on Richardson's extrapolation. Experiments are conducted on three problems in order to qualify the advantages of adaptive techniques relative to uniform mesh computations and the relative benefits of mesh moving and refinement. Key results indicate that local mesh refinement, with and without mesh moving, can provide reliable solutions at much lower computational cost than possible on uniform meshes; that mesh motion can be used to improve the results of uniform mesh solutions for a modest computational effort; that the cost of managing the tree data structure associated with refinement is small; and that a combination of mesh motion and refinement reliably produces solutions for the least cost per unit accuracy.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: Applied Numerical Mathematics (ISSN 0168-9274); p. 259-282
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  • 4
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    A new procedure for dynamic adaption of three-dimensional unstructured grids (1993)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: A new procedure is presented for the simultaneous coarsening and refinement of three-dimensional unstructured tetrahedral meshes. This algorithm allows for localized grid adaption that is used to capture aerodynamic flow features such as vortices and shock waves in helicopter flowfield simulations. The mesh-adaption algorithm is implemented in the C programming language and uses a data structure consisting of a series of dynamically-allocated linked lists. These lists allow the mesh connectivity to be rapidly reconstructed when individual mesh points are added and/or deleted. The algorithm allows the mesh to change in an anisotropic manner in order to efficiently resolve directional flow features. The procedure has been successfully implemented on a single processor of a Cray Y-MP computer. Two sample cases are presented involving three-dimensional transonic flow. Computed results show good agreement with conventional structured-grid solutions for the Euler equations.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: AIAA PAPER 93-0672 , RIACS-TR-93-01 , AD-A268651 , AIAA, Aerospace Sciences Meeting and Exhibit; Jan 11, 1993 - Jan 14, 1993; Reno, NV; United States|; 13 p.
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