Volume 41, pp. 306-327, 2014.

Finite element approximation of viscoelastic flow in a moving domain

Jason Howell, Hyesuk Lee, and Shuhan Xu

Abstract

In this work the problem of a viscoelastic fluid flow in a movable domain is considered. A numerical approximation scheme is developed based on the Arbitrary Lagrangian-Eulerian (ALE) formulation of the flow equations. The spatial discretization is accomplished by the finite element method, and the discontinuous Galerkin method is used for stress approximation. Both first and second order time-stepping schemes satisfying the geometric conservation law (GCL) are derived and analyzed, and numerical experiments that support the theoretical results are presented.

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Key words

Viscoelastic fluid flow, moving boundary, finite elements, fluid-structure interaction.

AMS subject classifications

65M60, 65M12.

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