Spatial and temporal stability issues for interfacial flows with surface tension

J. T. Beale, T. Y. Hou, J. S. Lowengrub, Michael Shelley

Research output: Contribution to journalArticle

Abstract

Many physically interesting problems involve the propagation of free surfaces in fluids with surface tension effects. Surface tensions is an ever-present physical effect that is often neglected due to the difficulties associated with its inclusion in the equations of motion. Accurate simulation of these interfaces presents a problem of considerable difficulty on several levels. First, even for stably stratified flows like water waves, it turns out that straightforward spatial discretizations (of the boundary integral formulation) generate numerical instability. Second, surface tension introduces a large number of derivatives through the Laplace-Young boundary condition. This induces severe time step restrictions for explicit time integration methods. In this paper, we present a class of stable spatial discretizations and we present a reformulation of the equations of motion that make apparent how to remove the high order time step restrictions introduced by the surface tension. This paper is a review of the results given in [1,2].

Original languageEnglish (US)
Pages (from-to)1-27
Number of pages27
JournalMathematical and Computer Modelling
Volume20
Issue number10-11
DOIs
StatePublished - 1994

Fingerprint

Interfacial Flow
Surface Tension
Surface tension
Equations of motion
Equations of Motion
Discretization
Explicit Time Integration
Restriction
Stratified Flow
Numerical Instability
Boundary Integral
Water waves
Water Waves
Reformulation
Laplace
Free Surface
Inclusion
Boundary conditions
Propagation
Higher Order

Keywords

  • Interfacial flows
  • Stability
  • Surface tension

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Information Systems and Management
  • Control and Systems Engineering
  • Applied Mathematics
  • Computational Mathematics
  • Modeling and Simulation

Cite this

Spatial and temporal stability issues for interfacial flows with surface tension. / Beale, J. T.; Hou, T. Y.; Lowengrub, J. S.; Shelley, Michael.

In: Mathematical and Computer Modelling, Vol. 20, No. 10-11, 1994, p. 1-27.

Research output: Contribution to journalArticle

Beale, J. T. ; Hou, T. Y. ; Lowengrub, J. S. ; Shelley, Michael. / Spatial and temporal stability issues for interfacial flows with surface tension. In: Mathematical and Computer Modelling. 1994 ; Vol. 20, No. 10-11. pp. 1-27.
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