High-order centered difference methods with sharp shock resolution | Zendy

Bertil Gustafsson | Zendy; Pelle Olsson | Zendy

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High-order centered difference methods with sharp shock resolution

Author(s) -

Bertil Gustafsson,

Pelle Olsson

Publication year - 1996

Publication title -

journal of scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.53

H-Index - 80

eISSN - 1573-7691

pISSN - 0885-7474

DOI - 10.1007/bf02088817

Subject(s) - mathematics , shock (circulatory) , conservation law , simple (philosophy) , resolution (logic) , riemann problem , finite difference , mathematical analysis , viscosity , order (exchange) , riemann hypothesis , finite difference method , shock wave , point (geometry) , mechanics , geometry , physics , thermodynamics , computer science , medicine , philosophy , epistemology , finance , artificial intelligence , economics

High-order centered finite difference approximations of hyperbolic conservation laws are considered. Different ways of adding artificial viscosity to obtain sharp shock resolution are proposed. For the Riemann problem simple explicit formulas for obtaining stationary one- and two-point shocks are presented. This can be done for any order of accuracy. It is shown that the addition of artificial viscosity is equivalent to ensuring the Laxk-shock condition. Numerical experiments verify the theoretical results.

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