Numerical Investigations Concerning the Strategy of Control of the Spatial Order of Approximation Along a Fitted Gas–Liquid Interface

C. Dickopp () and J. Ballmann ()
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C. Dickopp: Lehr- und Forschungsgebiet f. Mechanik der RWTH Aachen
J. Ballmann: RWTH Aachen University, Mechanics Department Lehr- und Forschungsgebiet für Mechanik

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2008, pp 449-456 from Springer

Abstract: With the motivation to simulate a collapsing gas or vapor bubble in a liquid, a finite element method using bilinear or piecewise constant shape and test functions for the spatial discretization and several Runge–Kutta methods for the time integration has been developed. The method approximates the solution of the Euler or Navier–Stokes equations in a Lagrangian formulation on an unstructured, moving grid in two space dimensions to fit the bubble–liquid interface. The nonlinear stability of the method is achieved by an improvement of the FCT-strategy for the control of the spatial order of approximation. A series of numerical investigations indicates a strong dependence between the numerical solution of the model problem of a collapsing single bubble and the strategy of control of the spatial order of approximation along the bubble wall.

Keywords: Liquid Interface; Nonlinear Stabilization; Jump Condition; Order Scheme; Single Bubble (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-75712-2_42

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DOI: 10.1007/978-3-540-75712-2_42

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