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Time Discretization for Capillary Flow: Beyond Backward Euler

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Transport Processes at Fluidic Interfaces

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

Development and analysis of numerical methods for two-phase flow has mainly focussed on spatial aspects of the discretization so far. In turn, most of the methods available are of first order in time at most and only conditionally stable. For many applications, however, these shortcomings may constitute the computational bottleneck, since both disadvantages dictate very small time step sizes in order to arrive at a decent approximation of the underlying problem. In this article we therefore focus on the time discretization of capillary free surface flows with the following features: higher order in time convergence, unconditional stability and low dissipativity. Applying the method of lines we use stiff integrators from the class of Rosenbrock and W-methods. As an alternative, a space-time Galerkin method is presented. These methods are compared computationally for examples of one- and two-phase capillary flows.

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Authors and Affiliations

  1. CD-adapco, Nürnberg Office, Nürnberg, Germany

    Stephan Weller

  2. Department Mathematics, Universität Erlangen-Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany

    Eberhard Bänsch

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  1. Stephan Weller
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  2. Eberhard Bänsch
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Correspondence to Eberhard Bänsch .

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Editors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt , Darmstadt, Germany

    Dieter Bothe

  2. Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Arnold Reusken

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Weller, S., Bänsch, E. (2017). Time Discretization for Capillary Flow: Beyond Backward Euler. In: Bothe, D., Reusken, A. (eds) Transport Processes at Fluidic Interfaces. Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-56602-3_5

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