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Preprints of the Keldysh Institute of Applied Mathematics, 2023, 017, 27 pp.
DOI: https://doi.org/10.20948/prepr-2023-17
(Mi ipmp3140)
 

Solution of convection-diffusion equations by local discontinuous Galerkin method

I. R. Khaytaliev, E. V. Shilnikov
References:
Abstract: In the work, the discontinuous Galerkin method (LDG) is applied to solving linear and nonlinear convection-diffusion problems. The idea of this method is to transform high-order equations into a system of first-order equations, and then apply the classical discontinuous Galerkin method (DG) to this system. An orthogonal system of Legendre polynomials is chosen as the system of basis functions. The cases of both continuous and discontinuous solutions of the problem are considered. The dependence of the accuracy and stability of the method on the step of the spatial grid and the number of basis functions is investigated. The application of parallel computing to the algorithm is investigated. In the future, it is proposed to apply the LRG method for solving the problems of modeling gas mixtures flows.
Keywords: local discontinuous Galerkin method, Legendre polynomials, Burgers' equation, solution accuracy, algorithm stability, parallel calculations.
Document Type: Preprint
Language: Russian
Citation: I. R. Khaytaliev, E. V. Shilnikov, “Solution of convection-diffusion equations by local discontinuous Galerkin method”, Keldysh Institute preprints, 2023, 017, 27 pp.
Citation in format AMSBIB
\Bibitem{KhaShi23}
\by I.~R.~Khaytaliev, E.~V.~Shilnikov
\paper Solution of convection-diffusion equations by local discontinuous Galerkin method
\jour Keldysh Institute preprints
\yr 2023
\papernumber 017
\totalpages 27
\mathnet{http://mi.mathnet.ru/ipmp3140}
\crossref{https://doi.org/10.20948/prepr-2023-17}
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