Immersed interface methods for Stokes flow with elastic boundaries or surface tension

Journal Article · Thu May 01 04:00:00 EDT 1997 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/S1064827595282532· OSTI ID:509277

Leveque, R J ^[1]; Li, Z ^[2]

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1. Univ. of Washington, Seattle, WA (United States)
2. Mississippi State Univ., Mississippi State, MS (United States). Dept. of Mathematics and Statistics

A second-order accurate interface tracking method for the solution of incompressible Stokes flow problems with moving interfaces on a uniform Cartesian grid is presented. The interface may consist of an elastic boundary immersed in the fluid or an interface between two different fluids. The interface is represented by a cubic spline along which the singularly supported elastic or surface tension force can be computed. The Stokes equations are then discretized using the second-order accurate finite difference methods for elliptic equations with singular sources developed in a previous paper. The resulting velocities are interpolated to the interface to determine the motion of the interface. An implicit quasi-Newton method is developed that allows reasonable time steps to be used.

• Sponsoring Organization: USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• DOE Contract Number: FG06-93ER25181
• OSTI ID: 509277
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 3 Vol. 18; ISSN 1064-8275; ISSN SJOCE3
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS
CALCULATION METHODS
CARTESIAN COORDINATES
DIFFERENTIAL EQUATIONS
FINITE ELEMENT METHOD
INCOMPRESSIBLE FLOW
STOKES LAW