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A generic framework for time-stepping partial differential equations (PDEs): general linear methods, object-oriented implementation and application to fluid problems

P. E. J. Vos ; Claes Eskilsson (Institutionen för sjöfart och marin teknik, Hydromekanik) ; A. Bolis ; S. Chun ; R. M. Kirby ; S. J. Sherwin
International Journal of Computational Fluid Dynamics (1061-8562). Vol. 25 (2011), 3, p. 107-125.
[Artikel, refereegranskad vetenskaplig]

Time-stepping algorithms and their implementations are a critical component within the solution of time-dependent partial differential equations (PDEs). In this article, we present a generic framework - both in terms of algorithms and implementations - that allows an almost seamless switch between various explicit, implicit and implicit-explicit (IMEX) time-stepping methods. We put particular emphasis on how to incorporate time-dependent boundary conditions, an issue that goes beyond classical ODE theory but which plays an important role in the time-stepping of the PDEs arising in computational fluid dynamics. Our algorithm is based upon J.C. Butcher's unifying concept of general linear methods that we have extended to accommodate the family of IMEX schemes that are often used in engineering practice. In the article, we discuss design considerations and present an object-oriented implementation. Finally, we illustrate the use of the framework by applications to a model problem as well as to more complex fluid problems.

Nyckelord: time-stepping methods, Method of Lines, IMEX-schemes, object-oriented, implementation, time-dependent boundary conditions, fluid problems, runge-kutta methods, dimsims

Denna post skapades 2011-06-30. Senast ändrad 2012-01-17.
CPL Pubid: 142748


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Institutioner (Chalmers)

Institutionen för sjöfart och marin teknik, Hydromekanik (2005-2011)


Teknisk mekanik

Chalmers infrastruktur