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  • 1
    Publication Date: 2013-08-31
    Description: In this work the compressible Euler equations are solved using finite volume techniques on unstructured grids. The spatial discretization employs a central difference approximation augmented by dissipative terms. Temporal discretization is done using a multistage Runge-Kutta scheme. A multigrid technique is used to accelerate convergence to steady state. The coarse grids are derived directly from the given fine grid through agglomeration of the control volumes. This agglomeration is accomplished by using a greedy-type algorithm and is done in such a way that the load, which is proportional to the number of edges, goes down by nearly a factor of 4 when moving from a fine to a coarse grid. The agglomeration algorithm has been implemented and the grids have been tested in a multigrid code. An area-weighted restriction is applied when moving from fine to coarse grids while a trivial injection is used for prolongation. Across a range of geometries and flows, it is shown that the agglomeration multigrid scheme compares very favorably with an unstructured multigrid algorithm that makes use of independent coarse meshes, both in terms of convergence and elapsed times.
    Keywords: NUMERICAL ANALYSIS
    Type: The Sixth Copper Mountain Conference on Multigrid Methods, Part 2; p 649-662
    Format: application/pdf
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  • 2
    Publication Date: 2016-06-07
    Description: The problem of generating local mesh refinements when solving time dependent partial differential equations was examined. The problem of creating an appropriate grid, given a mesh function h defined over the spatial domain is discussed. A data structure which permits efficient use of the resulting grid is described. A good choice for h is an estimate of the local truncation error, and several ways to estimate it are discussed. The efficiency and implementation problems of these error estimates were compared.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA. Langley Research Center Numerical Grid Generation Tech.; p 181-188
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  • 3
    Publication Date: 2019-06-28
    Description: The inviscid Euler equations in complicated geometries are solved using a Cartesian grid. This requires solid wall boundary conditions in the irregular grid cells near the boundary. Since these cells may be orders of magnitude smaller than the regular grid cells, stability is a primary concern. An approach to this problem is presented and its use is illustrated.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-182048 , NAS 1.26:182048 , ICASE-90-37 , AD-A223152
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  • 4
    Publication Date: 2019-06-28
    Description: A method of adaptive grid refinement for the solution of the steady Euler equations for transonic flow is presented. Algorithm automatically decides where the coarse grid accuracy is insufficient, and creates locally uniform refined grids in these regions. This typically occurs at the leading and trailing edges. The solution is then integrated to steady state using the same integrator (FLO52) in the interior of each grid. The boundary conditions needed on the fine grids are examined and the importance of treating the fine/coarse grid inerface conservatively is discussed. Numerical results are presented.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-173161 , NAS 1.26:173161 , DE84-004988 , DOE/ER-03077/202
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  • 5
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    In:  Other Sources
    Publication Date: 2019-07-12
    Description: A study is conducted of the stability of mesh refinement in space and time for several different interface equations and finite-difference approximations. First, a root condition which implies stability for the initial-boundary value problem for this type of interface is derived. From the root condition, the stability of several interface equations is proved, using the maximum principle. In some cases, the final verification steps can be done analytically; in other cases, a simple computer program has been written to check the condition for values of a parameter along the boundary of the unit circle. Using this method, stability for Lax-Wendroff with all the interface conditions considered, and for Leapfrog with interpolation interface conditions when the fine and coarse grids overlap is proved.
    Keywords: NUMERICAL ANALYSIS
    Type: Mathematics of Computation (ISSN 0025-5718); 45; 301-318
    Format: text
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