A Stabilized High-Order Spectral Model With Adaptive Residual-Based Artificial Viscosity for Fully-Nonlinear Free-Surface Flow

Abstract

In the present work, a stabilized High-Order Spectral (HOS) model with adaptive residual-based artificial viscosity (RAV) has been developed for performance enhancement in fully-nonlinear free-surface flow simulation. To suppress the numerical instability caused by the nonlinear wave-wave interactions, that is, the nonlinear mode-coupling between eigen-modes, with an explicit time-domain integrator, additional estimations about the numerical residuals of free-surface elevation and free-surface potential with their backward histories have been carried out for stability-indicating and artificial viscous terms have been suggested to balance such unphysical energy-accumulation, especially for under-resolved wave components. Upon the normalized free-surface residuals as the scales of artificial viscosity, an even-order dissipation term has been assembled for energy suppression. To retain the overall explicit algorithm, such additional dissipation has been considered in an operator-splitting manner. For the proposed dissipation algorithm, it has been shown that the present residual-based artificial energy-suppression holds the spectral-vanishing property because of its wave-number-related normalization in wave-number space. With such spectral normalization, the dissipation for the lower-wave-number well-resolved wave components has been well-controlled with the increase of dissipation order. Compared with the commonly used spectral-filtering-based stabilization algorithm, where the energy suppression within single-step free-surface prediction shows independence from the temporal increment ($\delta t$), the developed residual-based algorithm holds a solution-adaptive property, leading to an enhanced convergence performance of the free-surface model with its stabilization term tightly coupled to $\delta t$. To check the performance of the present RAV-HOS model, a series of classical benchmarks, both numerical and experimental, have been reproduced, and a HOS-based Numerical-Wave-Tank (HOS-NWT) has been built as a preparation for our further investigations into wave-wave and wave-structure interactions. With the confirmation of both robustness and accuracy of the proposed stabilized HOS model, a promising prospect for its further application in oceanic, offshore, and marine engineering as an efficient free-surface simulator has been expected.