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.

翻译：本文阐述了龙格-库塔间断伽辽金（RKDG）方法在模拟运动流体中超声波对流传播时的时间与内存高效应用。本研究特别针对依赖声波传播测量流体流量的渡越时间超声波流量计的分析问题。因此，对超声波输运相关物理过程进行精确高效的模拟，对于研究和改进此类设备至关重要。从线性化欧拉方程（LEE）模型的描述出发，在阐述双曲系统显式时间DG方法的一般理论后，我们论证了谱基函数使用的合理性，并提出了一种新型高精度边界处理方法。该方法通过分析边界表面的入射波方向，实现了吸收性与阻抗性壁面的精确施加。所提出的实施方案兼具精度与效率，适用于声波传播的工业应用场景。