Level set function–based immersed interface method and benchmark solutions for fluid flexible‐structure interaction

Abstract

SummaryUsing a hybrid Lagrangian‐Eulerian approach, a level set function–based immersed interface method (LS‐IIM) is proposed for the interaction of a flexible body immersed in a fluid flow. The LS‐IIM involves finite volume method for the fluid solver, Galerkin finite element method for the structural solver, and a block‐iterative partitioned method–based fully implicit coupling between the two solvers. The novelty of the proposed method is a level set function–based direct implementation of fluid‐solid interface boundary conditions in both the solvers. Another novelty is the computation of the level set function from a geometric method instead of differential equations commonly used in level set methods—the novel geometric as compared to the traditional method is found to be more accurate and less time‐consuming. The LS‐IIM is demonstrated as second‐order accurate. Verification study is presented first separately for both the solvers and then together for four fluid‐structure interaction (FSI) problems, with different levels of complexity including lid‐driven flow, channel flow, and free‐stream flow. Benchmark solutions are presented for two class of FSI problems: first, easy to set up and less time‐consuming and, second, a reasonably challenging and complex FSI problem involving sharp edges and forced‐motion of the flexible structure. The benchmark solutions are proposed at steady state for the first problem, after a verification study with two open‐source solvers and, at periodic state, after a validation with published experimental results for the second problem. Our benchmark solutions may be useful for verification study in future.