Bänsch E, Weller S (2012)

**Publication Type:** Book chapter / Article in edited volumes

**Publication year:** 2012

**Edited Volumes:** ALGORITMY 2012, 19th Conference on Scientific Computing

**Pages Range:** 331-341

The fundamental problems in the numerical approximation of multiphase systems, or more generally speaking, in the treatment of flows with capillary free boundaries are the representation of the free surface, evaluating the curvature, handling of discontinuities, most importantly the pressure jump, and time discretization strategies for the decoupling of flow computation and geometry.

While for the first three items there exists a vast literature and many techniques developed over the last two decades, the last problem of how to efficiently treat the time discretization has been widely ignored. The majority of the existing approaches just decouple the flow field from the geometry by a simple segregated approach, i.e. evaluating the geometric quantities from the previous time step. These strategy leads to a) a severe capillary CFL condition and b) is of first order in time at most. Existing semi-implicit discretizations exist that overcome problem a), but are still first order only and rather dissipative in certain situations.We compare different existing time discretization schemes for the fully coupled system of Navier-Stokes and the phase boundary condition. Time discretization might be semi-implicit, fully implicit or linearly implicit. The methods are applied to a simple test case where experimental order of convergence and numerical dissipation can be compared relatively easily.

Eberhard Bänsch
Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen)
Stephan Weller
Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen)

**APA:**

Bänsch, E., & Weller, S. (2012). A comparison of several time discretization methods for free surface flows. In Angela Handlovicova, Zuzana Minarechova, Daniel Sevcovic (Eds.), *ALGORITMY 2012, 19th Conference on Scientific Computing.* (pp. 331-341).

**MLA:**

Bänsch, Eberhard, and Stephan Weller. "A comparison of several time discretization methods for free surface flows." *ALGORITMY 2012, 19th Conference on Scientific Computing.* Ed. Angela Handlovicova, Zuzana Minarechova, Daniel Sevcovic, 2012. 331-341.

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