An immersed boundary level-set based approach for fluid-shell interaction with impact.

Abstract

Fluid-shell interaction modeling is a challenging problem with application to several engineering elds. In this research we develop a partitioned algorithm for large displacements uid-shell coupling with impact. The structure is modeled in a total La- grangian description, using a novel shell nite element formulation to deal with geometric nonlinear dynamics of thin or thick shells. This formulation is based on the principle of minimum potential energy considering positions and generalized unconstrained vectors as nodal parameters, instead of displacements and rotations. As a consequence, the formu- lation eliminates the need for large rotation approximations and presents constant mass matrix, allowing the use of Newmark time integrator for the nonlinear problem. The Newton-Raphson method is employed to solve the resulting nonlinear system and contact between structures is modeled by enforcing non-penetration conditions based on a signed distance function. The ow is assumed to be compressible and the uid dynamics solver is explicit with time integration based on characteristics. The uid governing equations are written in the Eulerian description generating a xed mesh method. The coupled prob- lem is solved by using an embedded boundary technique where the uid-shell interface is tracked inside the unstructured uid mesh by level sets of a signed distance to bound- ary function. The versatility and e ciency of the proposed approach is demonstrated by selected three- dimensional examples.