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TsAGI Science Journal

ISSN Druckformat: 1948-2590
ISSN Online: 1948-2604

TsAGI Science Journal

DOI: 10.1615/TsAGISciJ.v40.i4.20
pages 419-436

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

Andrey Viktorovich Wolkov
Central Aerohydrodynamic Institute (TsAGI), 1 Zhukovsky Str., Zhukovsky, Moscow Region, 140180, Russian Federation
Sergey Vladimirovich Lyapunov
Central Aerohydrodynamic Institute (TsAGI) 1, Zhukovsky str., Zhukovsky, 140180, Moscow region, Russia

ABSTRAKT

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.


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