Abstract
To solve various-scale problems with a complex configuration of surfaces, in which it is impossible to obtain a solution only by refining the mesh, it is necessary to use high-precision numerical methods. One of the methods that guarantee high accuracy of the obtained solution is the discontinuous Galerkin method. The solution of real problems of supersonic aerodynamics is characterized by the presence of areas of high gradients; therefore, it becomes necessary to use special limiting operators. In this chapter, a generalization of the Cockburn limiter to various types of cells is constructed, as well as a new transformation for numerical Gaussian integration over a cell of the type of a quadrangular pyramid is proposed.
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The work was carried out with support by the Russian Science Foundation (grant no. 21-11-00198).
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Tishkin, V.F., Ladonkina, M.E. (2022). Some Features of DG Method Application for Solving Gas Dynamics Problems. In: Favorskaya, M.N., Nikitin, I.S., Severina, N.S. (eds) Advances in Theory and Practice of Computational Mechanics. Smart Innovation, Systems and Technologies, vol 274. Springer, Singapore. https://doi.org/10.1007/978-981-16-8926-0_4
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