A Simple Parallel Solution Method for the Navier–Stokes Cahn–Hilliard Equations

Nadja Adam, Florian Franke and Sebastian Aland
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Nadja Adam: Faculty of Informatics/Mathematics, HTW Dresden, Friedrich-List-Platz 1, 01069 Dresden, Germany
Florian Franke: Faculty of Informatics/Mathematics, HTW Dresden, Friedrich-List-Platz 1, 01069 Dresden, Germany
Sebastian Aland: Faculty of Informatics/Mathematics, HTW Dresden, Friedrich-List-Platz 1, 01069 Dresden, Germany

Mathematics, 2020, vol. 8, issue 8, 1-14

Abstract: 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.

Keywords: two-phase flow; diffuse interface; phase field; Navier–Stokes; Cahn–Hilliard (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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