Optimizing wave-generation and wave-damping in 3D-flow simulations with implicit relaxation-zones

TL;DR

This paper presents an analytical method to optimize implicit relaxation zones in 3D flow simulations with free-surface waves, reducing wave reflections and improving simulation accuracy.

Contribution

It introduces an analytical approach for optimizing relaxation zone parameters and compares it with simulation results, demonstrating its effectiveness and applicability in engineering practice.

Findings

Analytical predictions closely match simulation results, with less than 3.4% deviation.

Implicit relaxation zones can be viewed as a special case of forcing zones.

The approach effectively predicts upper limits for reflection coefficients.

Abstract

In finite-volume-based flow-simulations with free-surface waves, wave reflections at the domain boundaries can cause substantial errors in the results and must therefore be minimized. This can be achieved via `implicit relaxation zones', but only if the relaxation zone's case-dependent parameters are optimized. This work proposes an analytical approach for optimizing these parameters. The analytical predictions are compared against results from 2D-flow simulations for different water depths, flow solvers, and relaxation functions, and against results from 3D-flow simulations with strongly wave-reflecting bodies subjected to nonlinear free-surface waves. The present results demonstrate that the proposed approach satisfactorily predicts both the optimum parameter settings and the upper-limit for the corresponding reflection coefficients $C_{\mathrm{R}}$. Simulation results for $C_{\mathrm{R}}$ were mostly below or equal to the analytical predictions, but never more than $3.4\%$ larger. Therefore, the proposed approach can be recommended for engineering practice. Furthermore, it is shown that implicit relaxation zones can be considered as a special-case of forcing zones, a family of approaches which includes among others absorbing layers, damping zones and sponge layers. The commonalities and differences between these approaches are discussed, including to what extend the present findings are applicable to these other approaches and vice versa.