# Analytical Prediction of Reflection Coefficients for Wave Absorbing Layers

## TL;DR

This paper develops a theory to predict reflection coefficients in wave absorbing layers, enabling optimal parameter tuning to minimize wave reflections in finite-volume flow simulations across 1D, 2D, and 3D cases.

## Contribution

It introduces a novel theoretical framework for predicting reflection coefficients, extending from 1D to multi-dimensional waves, validated by flow simulations.

## Key findings

- Theory accurately predicts reflection coefficients.
- Simulation results confirm the theory's validity.
- Optimal tuning of absorbing layers reduces wave reflections.

## Abstract

In finite-volume-based flow simulations, absorbing layers are widely used to reduce pressure wave reflections at boundaries of the computational domain. A disadvantage of absorbing layers is that they contain case-dependent parameters; thus the question is how to optimally tune these parameters, so that a desired reduction of reflections can be obtained? As a step towards the answer of these questions, this article presents a theory which predicts reflection coefficients for absorbing layers. The theory is given for 1D-wave propagation and is then extended to 2D and 3D to cover waves of oblique incidence. The theory is validated via flow simulations of regular and irregular pressure waves in air and water, based on Navier-Stokes-type equations and the finite-volume method. Theory predictions and simulation results show good agreement. It is demonstrated how the theory can be used to optimally tune the absorbing layer parameters to minimize undesired wave reflection. Thus the theory has benefits for a wide range of applications of finite-volume-based flow simulations in industrial practice.