A finite element method for GPU-based elastic wave modelling in solid-fluid media using displacement fields

Abstract

Ultrasonic wave propagation and scattering involving both solids and fluids underpin many key configurations in non-destructive testing and underwater acoustics. The resulting interactions are highly dependent on both material parameters and geometries and are often 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. In this thesis, work is presented on simulating ultrasonic wave phenomena involving both solids and fluids, using the finite element method implemented on graphical processing units. The thesis beings with a literature review existing analytical and numerical methods as well as certain necessary building blocks and useful background information. A novel explicit time-domain finite element method for simulating ultrasonic waves interacting with fluid-solid interfaces is then introduced, allowing investigation of complex, industrially relevant configurations at scale and speed. The method is displacement-based, and relies on classical hourglassing control, in addition to a modified time-stepping scheme to damp out any 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 common in other approaches. It is thus compatible with typical elastodynamic finite element formulations and ready for implementation on a graphical processing unit. The method has been verified across a range of problems that involve millions of degrees of freedom from different fields, such as non-destructive testing and underwater acoustics, and across different scales, with frequencies of interest ranging from kHz to MHz. There is also a brief investigation on geometrical model refinement and some initial research and simulations conducted to extend this work in three dimensions.