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

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • C. Dickopp

    (Lehr- und Forschungsgebiet f. Mechanik der RWTH Aachen)

  • J. Ballmann

    (RWTH Aachen University, Mechanics Department Lehr- und Forschungsgebiet für Mechanik)

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.

Suggested Citation

  • C. Dickopp & J. Ballmann, 2008. "Numerical Investigations Concerning the Strategy of Control of the Spatial Order of Approximation Along a Fitted Gas–Liquid Interface," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 449-456, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_42
    DOI: 10.1007/978-3-540-75712-2_42
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