An extended finite element method with arbitrary interior discontinuous gradients is applied to two-phase immiscible flow problems. The discontinuity in the derivative of the velocity field is introduced by an enrichment with an extended basis whose gradient is discontinuous across the interface. Therefore, the finite element approximation can capture the discontinuities at the interface without requiring the mesh to conform to the interface, eliminating the need for remeshing. The equations for incompressible flow are solved by a fractional step method where the advection terms are stabilized by a characteristic Galerkin method. The phase interfaces are tracked by level set functions which are discretized by the same finite element mesh and are updated via a stabilized conservation law. The method is demonstrated in several examples.
An Extended Finite Element Method for Two-Phase Fluids
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, Dec. 4, 2001; final revision, Mar. 12, 2002. Associate Editor: T. E. Tezduyar. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Chair, Department of Mechanics and Environmental Engineering, University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
- Views Icon Views
- Share Icon Share
- Cite Icon Cite
- Search Site
Chessa, J., and Belytschko, T. (January 23, 2003). "An Extended Finite Element Method for Two-Phase Fluids ." ASME. J. Appl. Mech. January 2003; 70(1): 10–17. https://doi.org/10.1115/1.1526599
Download citation file:
- Ris (Zotero)
- Reference Manager