IB-WENO method for incompressible flow with elastic boundaries

Abstract

Abstract We present a new approach to compute the interaction between an elastic boundary and an incompressible viscous fluid, by integrating the immersed boundary method and a finite difference WENO scheme. The hybrid algorithm maintains simple and efficient treatment of the moving interface based on the immersed boundary formulation, and achieves high-order accuracy, with the WENO method and the Hodge decomposition technique employed, in the majority of the fluid domain that does not contain the interface. We demonstrate the performance of the proposed algorithm and its various numerical components through a number of computational examples.