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Time discretization for capillary flow: beyond backward Euler. (English) Zbl 1391.76588
Bothe, Dieter (ed.) et al., Transport processes at fluidic interfaces. Basel: Birkhäuser/Springer (ISBN 978-3-319-56601-6/hbk; 978-3-319-56602-3/ebook). Advances in Mathematical Fluid Mechanics, 121-143 (2017).
Summary: 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.
For the entire collection see [Zbl 1378.76006].
Reviewer: Reviewer (Berlin)
MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76M10 Finite element methods applied to problems in fluid mechanics
76D45 Capillarity (surface tension) for incompressible viscous fluids
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
Software:
ROS3P
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