A High Order Discontinuous Galerkin Method for Fluid-Structure Interaction

We describe a method for computing time-dependent solutions to the compressible Navier-Stokes equations coupled to a hyperelastic Neo-Hookean membrane model. The deforming domain is handled by introducing a continuous mapping between a fixed reference configuration and the time varying domain, and rewriting the Navier-Stokes equations as a conservation law for the independent variables in the reference configuration. The spatial discretization is carried out using the Discontinuous Galerkin method on unstructured meshes of triangles, and the membrane model is discretized with regular finite elements. The method uses an explicit smooth mapping for the entire domain which is dierentiated to obtain accurate grid velocities and deformation gradients. This mapping is constructed by a combination of spline interpolation and high order blending functions. Various examples are shown to illustrate the methods, and elastic and rigid membranes are compared.

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