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TsAGI Science Journal

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ISSN Печать: 1948-2590

ISSN Онлайн: 1948-2604

MONOTONIZATION OF THE FINITE ELEMENT METHOD IN THE PROBLEMS OF GAS DYNAMICS

Том 40, Выпуск 4, 2009, pp. 419-436
DOI: 10.1615/TsAGISciJ.v40.i4.20
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Краткое описание

The conservation law approximation method—the Galerkin finite element method with discontinuous basis functions (DG)—was modified by adding the λ parameter, which enables smooth control of the order of accuracy of the numerical scheme. Modification of the known finite element scheme allows for a smooth transition from a high-order-of-accuracy scheme to a monotonic scheme of the first order of accuracy in the areas of flow singularities. The original approach to the choice of the λ parameter is considered. The developed DG-λ scheme provides for the absence of nonphysical oscillations of the solution in the areas of flow singularities, which is shown by the solution of the model convection-diffusion problem and the calculation of flows described by Navier–Stokes equations. The possibility to obtain high-accuracy solutions on adapted unstructured grids is shown.

ЦИТИРОВАНО В
  1. Chernyshev Sergey L., A review of Russian computer modeling and validation in aerospace applications, Progress in Aerospace Sciences, 128, 2022. Crossref

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