A discontinuous galerkin approach for the numerical simulation of transit-time ultrasonic flowmeters

A Discontinuous Galerkin approach is presented for the numerical simulation of acoustic waves propagation in transit-time ultrasonic flowmeters with clamp-on transducers. In this configuration, the ultrasonic beam crosses multiple solid-solid and fluid-solid interfaces which generate complex physical phenomena with an important impact on the flow rate measurement. To capture all these phenomena, the employed physical model is based on the wave theory. The wave propagation in the fluid part is described by the linearized Euler equations and in the solid part by the equations of linear elasticity. Considering the good parallelization properties of the numerical method, the simulation code was implemented to run on graphical processing units. To validate it, several test cases are performed for both separated and coupled fluid-solid media. Furthermore, a study on the impact of pipe flow profiles on the flow rate measurement is carried out.