Stable Semi-Implicit Monolithic Scheme for Interaction Between Incompressible Neo-Hookean Structure and Navier-Stokes Fluid
Year: 2019
Author: Cornel Marius Murea
Journal of Mathematical Study, Vol. 52 (2019), Iss. 4 : pp. 448–469
Abstract
We present a monolithic algorithm for solving fluid-structure interaction. The Updated Lagrangian framework is used for the incompressible neo-hookean structure and Arbitrary Lagrangian Eulerian coordinate is employed for the Navier-Stokes equations. The algorithm uses a global mesh for the fluid-structure domain which is compatible with the fluid-structure interface. At each time step, a non-linear system is solved in a domain corresponding to the precedent time step. It is a semi-implicit algorithm in the sense that the velocity, the pressure are computed implicitly, but the domain is updated explicitly. Using one velocity field defined over the fluid-structure mesh, and globally continuous finite elements, the continuity of the velocity at the interface is automatically verified. The equation of the continuity of the stress at the interface does not appear in this formulation due to action and reaction principle. The stability in time is proved. A second algorithm is introduced where at each time step, only a linear system is solved in order to find the velocity and the pressure. Numerical experiments are presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v52n4.19.05
Journal of Mathematical Study, Vol. 52 (2019), Iss. 4 : pp. 448–469
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Fluid-structure interaction monolithic algorithm stability.