A Simple Parallel Solution Method for the Navier–Stokes Cahn–Hilliard Equations
We present a discretization method of the Navier–Stokes Cahn–Hilliard equations which offers an impressing simplicity, making it easy to implement a scalable parallel code from scratch. The method is based on a special pressure projection scheme with incomplete pressure iterations. The resulting sch...
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Veröffentlicht in: | Mathematics (Basel) 2020-08, Vol.8 (8), p.1224 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We present a discretization method of the Navier–Stokes Cahn–Hilliard equations which offers an impressing simplicity, making it easy to implement a scalable parallel code from scratch. The method is based on a special pressure projection scheme with incomplete pressure iterations. The resulting scheme admits solution by an explicit Euler method. Hence, all unknowns decouple, which enables a very simple implementation. This goes along with the opportunity of a straightforward parallelization, for example, by few lines of Open Multi-Processing (OpenMP) or Message Passing Interface (MPI) routines. Using a standard benchmark case of a rising bubble, we show that the method provides accurate results and good parallel scalability. |
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ISSN: | 2227-7390 2227-7390 |
DOI: | 10.3390/math8081224 |