An Adaptive Mesh Refinement Approach for Viscous Fluid-Structure Computations Using Eulerian Vertex-Based Finite Volume Methods

摘要

Embedded Boundary Methods (EBMs) for the solution of fluid and Fluid-Structure Interaction (FSI) problems are typically formulated in the Eulerian setting, which makes them especially attractive when the structure undergoes large structural motions and/or deformations, or topological changes. For viscous problems however, they suffer from a major drawback in that they do not track the boundary layers that form around embedded obstacles and therefore do not maintain them efficiently resolved. In this paper, this drawback is overcome using an Adaptive Mesh Refinement (AMR) approach based on the time-dependent distance from a computational cell to the nearest embedded surface which may deform and evolve in time. The proposed approach features a fast predictor-corrector algorithm for updating the distance to the wall that is particularly efficient for explicit-explicit time-stepping discretizations. These are preferred for highly nonlinear FSI computations such as those associated, for example, with the simulation of parachute inflation dynamics. For vertex-based finite volume computations performed on dual cells, AMR gives rise to non-conforming mesh configurations that complicate the semi-discretization process. The proposed AMR approach addresses this issue by appropriately managing the construction and destruction of edges, primal elements and dual cells, so that mesh conformity can be explicitly enforced during the mesh adaptation process. It is illustrated here with preliminary results obtained for the simulation of the inflation of a membrane in a supersonic airstream using the EBM for FSI computations known as FIVER (Finite Volume method with Exact two-material Riemann problems).