An Embedded Domain Technique Based on Level-Sets for Finite Element Method (FEM) Fluid-Shell Coupling

Abstract

This paper presents a robust level-set-based approach that integrates a Lagrangian shell finite element
solver and an Eulerian finite element high speed fluid flow solver, with no need for mesh adaptation, where the fluid representation relies on a fixed unstructured mesh larger or equal to the initial fluid domain. The Eulerian fluid solver is based on a fully explicit scheme, with time integration based on characteristics over an unstructured mesh of four nodes tetrahedral finite elements. The structure is modeled using a positional finite element method formulation to deal with geometrical nonlinear dynamics of
shells based on the minimum potential energy theorem written regarding nodal positions and generalized
unconstrained vectors, not displacements and rotations, avoiding the use of large rotation approximations.
The fluid-shell interface inside the fluid mesh is tracked with level sets of a boundary signed distance function. The conservation laws and continuity at the interface are enforced by applying proper interface boundary conditions to the fluid and shell solvers at the beginning of each time step. For the fluid case this is done by enforcing values over the nodes outside the domain which are connected to
nodes inside, together with a signed distance based slope limiter that also changes velocities values on inside nodes settled very close to the boundary avoiding stability problems when most of the element volume is outside the structural region.