Enhanced Runge-Kutta Discontinuous Galerkin Method for Ultrasound Propagation in Transit-Time Flow Meters

TL;DR

This paper presents an efficient high-accuracy Runge-Kutta discontinuous Galerkin method for simulating ultrasound wave propagation in moving fluids, specifically improving transit-time ultrasonic flow meters.

Contribution

It introduces a novel spectral basis and boundary treatment for hyperbolic systems, enhancing simulation accuracy and efficiency for industrial ultrasonic applications.

Findings

Accurate simulation of ultrasound propagation in fluids.

Efficient implementation suitable for industrial use.

Improved boundary condition handling for wave incident angles.

Abstract

We illustrate a time and memory efficient application of Runge-Kutta discontinuous Galerkin (RKDG) methods for the simulation of the ultrasounds advection in moving fluids. In particular, this study addresses to the analysis of transit-time ultrasonic meters which rely on the propagation of acoustic waves to measure fluids flow rate. Accurate and efficient simulations of the physics related to the transport of ultrasounds are therefore crucial for studying and enhancing these devices. Starting from the description of the linearized Euler equations (LEE) model and presenting the general theory of explicit-time DG methods for hyperbolic systems, we then motivate the use of a spectral basis and introduce a novel high-accuracy method for the imposition of absorbing and resistive walls which analyses the incident wave direction across the boundary surface. The proposed implementation is both accurate and efficient, making it suitable for industrial applications of acoustic wave propagation.