A Nodal Immersed Finite Element-Finite Difference Method

The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between fluid and an structure. This uses element (FE) approximate the stresses forces on structural mesh (FD) momentum of entire fluid-structure system Cartesian grid. fundamental used by this follows boundary framework for interaction (FSI), in which force spreading operator prolongs grid, velocity interpolation restricts field defined that grid back onto mesh. Force both require projecting data space. Consequently, evaluating either coupling requires solving matrix equation at every time step. Mass lumping, projection matrices are replaced diagonal approximations, has potential accelerate considerably. Constructing operators also determining locations structure where velocities sampled. Here we show sampling nodes equivalent using lumped mass operators. A key theoretical result our analysis if these approaches together, IFED permits use derived from nodal quadrature rules any standard interpolatory element. different FE methods, specialized treatments accommodate lumping with higher-order shape functions. Our results confirmed numerical benchmarks, including solid mechanics tests examination dynamic model bioprosthetic heart valve.