Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 107-125 |
| Number of pages | 19 |
| Journal | International Journal of Computational Fluid Dynamics |
| Volume | 25 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2011 Mar 1 |
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All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Aerospace Engineering
- Condensed Matter Physics
- Energy Engineering and Power Technology
- Mechanics of Materials
- Mechanical Engineering
Cite this
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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. / Vos, Peter E.J.; Eskilsson, Claes; Bolis, Alessandro; Chun, Sehun; Kirby, Robert M.; Sherwin, Spencer J.
In: International Journal of Computational Fluid Dynamics, Vol. 25, No. 3, 01.03.2011, p. 107-125.Research output: Contribution to journal › Article
TY - JOUR
T1 - A generic framework for time-stepping partial differential equations (PDEs)
T2 - General linear methods, object-oriented implementation and application to fluid problems
AU - Vos, Peter E.J.
AU - Eskilsson, Claes
AU - Bolis, Alessandro
AU - Chun, Sehun
AU - Kirby, Robert M.
AU - Sherwin, Spencer J.
PY - 2011/3/1
Y1 - 2011/3/1
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=79958088220&partnerID=8YFLogxK
U2 - 10.1080/10618562.2011.575368
DO - 10.1080/10618562.2011.575368
M3 - Article
VL - 25
SP - 107
EP - 125
JO - International Journal of Computational Fluid Dynamics
JF - International Journal of Computational Fluid Dynamics
SN - 1061-8562
IS - 3
ER -