Solution of Fluid-Structure Interaction Problems using a Discontinuous Galerkin Technique

Abstract

The present work aims to address the problem of fluid-structure interaction using a discontinuous Galerkin approach. Starting from the Navier-Stokes equations on a fixed domain, an arbitrary Lagrangian Eulerian (ALE) approach is used to derive the equations for the deforming domain. A geometric conservation law (GCL) is then introduced, which guarantees freestream preservation of the numerical scheme. The space discretization is performed using a discontinuous Galerkin method and time integration is performed using either an explicit four stage Runge-Kutta scheme or an implicit BDF2 scheme. The mapping parameters for the ALE formulation are then obtained using algorithms based on radial basis functions (RBF) or linear elasticity. These strategies are robust and can be applied to bodies with arbitrary shapes and undergoing arbitrary motions. The robustnesss and accuracy of the ALE scheme coupled with these mapping strategies is then demonstrated by solving some model problems. The ability of the scheme to handle complex flow problems is demonstrated by analyzing the low Reynolds number flow over an oscillating circular cylinder.