Family of central bicompact schemes with spectral resolution property for hyperbolic equations

Чикиткин, А. В.; Rogov, B. V.

doi:10.1016/j.apnum.2019.03.007

Cited by 19 publications

(2 citation statements)

References 24 publications

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“…Bicompact schemes combine several positive properties. They have the fourth order of accuracy in space, which can be increased to the sixth, eighth, and so on (see [10]). At the same time, the difference order of the bicompact schemes' equations in the independent space variables coincides with the order of the partial differential equations to be solved.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, bicompact schemes preserve their high order of accuracy in space on highly nonuniform meshes, since the spatial stencil of the schemes occupies a single mesh cell. In the dispersion and dissipation properties, bicompact schemes are superior to many well-known finite-difference and compact schemes [10,11]. Finally, bicompact schemes can be efficiently implemented by applying space marching computation, including its parallel version [12].…”

Section: Introductionmentioning

confidence: 99%

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Bicompact schemes for multidimensional hyperbolic equations on Cartesian meshes with solution-based AMR

Bragin

Rogov

2019

KIAM Prepr.

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Recommended form of bibliographic references: Bragin M.D., Rogov B.V. Bicompact schemes for multidimensional hyperbolic equations on Cartesian meshes with solution-based AMR // Keldysh Institute Michael Dmitrievich Bragin, Boris Vadimovich RogovBicompact schemes for multidimensional hyperbolic equations on Cartesian meshes with solution-based AMR High-order bicompact schemes for hyperbolic equations on Cartesian meshes with solution-based adaptive mesh refinement are constructed. The algorithm for implementation of these schemes on such meshes is described in detail. A new solution-based criteria of mesh refinement is proposed. Bicompact schemes with this refinement criteria are tested on the two-dimensional problem of compactly supported pulse advection and the two-dimensional Sedov blast wave problem. It is shown, that the design of bicompact schemes allows them to be implemented on meshes of such class with good accuracy of the computed solution ensured.Keywords: bicompact schemes, high-order schemes, hyperbolic equations, adaptive mesh refinement.Брагин М. Д., Рогов Б. В. Бикомпактные схемы для многомерных уравнений гиперболического типа на декартовых сетках с адаптацией к решениюДля уравнений гиперболического типа построены высокоточные бикомпактные схемы на декартовых сетках с адаптацией к решению. Подробно описан алгоритм реализации бикомпактных схем на таких сетках. Предложен новый критерий адаптации сетки к решению. Бикомпактные схемы с этим критерием адаптации проверены на двумерной задаче о переносе финитного импульса и двумерной задаче Седова о сильном взрыве в идеальном газе. Показано, что конструкция бикомпактных схем допускает счет на сетках данного класса, обеспечивая при этом хорошую точность вычисляемого решения.Ключевые слова: бикомпактные схемы, высокоточные схемы, гиперболические уравнения, сетки с адаптивным измельчением.

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Section: Introductionmentioning

confidence: 99%