A displacement-based finite element formulation for solving elastic wave problems in coupled fluid-solid media on a GPU

Abstract

Ultrasonic wave propagation and scattering involving both solids and fluids underpins many key configurations in non-destructive testing and underwater acoustics. The resulting interactions are highly dependent on both material parameters and geometries and are difficult and expensive to investigate experimentally. Modelling capabilities are often used to overcome this, but these are also complex and computationally expensive due to the complexity of the fluid-solid interactions. We introduce a novel explicit time-domain finite element method for simulating ultrasonic waves interacting with fluid-solid interfaces. The method is displacement-based, and relies on classical hourglassing control, in addition to a modified time-stepping scheme to damping out shear motion in an inviscid fluid. One of the key benefits of the displacement-based approach is that nodes in the fluid have the same number of degrees of freedom as those in the solid. Therefore defining a fluid-solid model is as easy as defining an all-fluid or all-solid model, avoiding the need for any special treatments at the interfaces. It is thus compatible with typical elastodynamic finite element formulations and ready for implementation on a graphical processing unit. We verified the method across a range of problems involving millions of degrees of freedom in fields such as non-destructive testing and underwater acoustics.