{"title":"Application of the Local Discontinuous Galerkin Method to the Solution of the Quasi-Gas Dynamic System of Equations","authors":"E. V. Shilnikov, I. R. Khaytaliev","doi":"10.1134/s207004822307013x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The solution of a quasi-gas dynamic (QGD) system of equations using the local discontinuous Galerkin method (LDG) is considered. One-dimensional Riemann discontinuity problems with known exact solutions are solved. Strong discontinuities are present in the solutions of the problems. Therefore, to ensure the monotonicity of the solution obtained by the LDG method, the so-called slope limiters, or limiters, are introduced. A “moment” limiter is chosen that preserves as high an order as possible. The limiter is modified to smooth the oscillations in the areas where the solution is constant.</p>","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Models and Computer Simulations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s207004822307013x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
The solution of a quasi-gas dynamic (QGD) system of equations using the local discontinuous Galerkin method (LDG) is considered. One-dimensional Riemann discontinuity problems with known exact solutions are solved. Strong discontinuities are present in the solutions of the problems. Therefore, to ensure the monotonicity of the solution obtained by the LDG method, the so-called slope limiters, or limiters, are introduced. A “moment” limiter is chosen that preserves as high an order as possible. The limiter is modified to smooth the oscillations in the areas where the solution is constant.
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Mathematical Models and Computer Simulations is a journal that publishes high-quality and original articles at the forefront of development of mathematical models, numerical methods, computer-assisted studies in science and engineering with the potential for impact across the sciences, and construction of massively parallel codes for supercomputers. The problem-oriented papers are devoted to various problems including industrial mathematics, numerical simulation in multiscale and multiphysics, materials science, chemistry, economics, social, and life sciences.
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