A coupled local smoothing finite element method for diminishing dispersion error in underwater noise problems

Abstract

A standard finite element method (FEM) is hindered by numerical dispersion error and fails to achieve accurate solutions for underwater noise prediction at large wave numbers. This study develops an advanced FEM known as the coupled local smoothing FEM (CLS-FEM) to address this issue. This methodology integrates the local smoothing FEM (LS-FEM) with the modified Dirichlet-to-Neumann boundary condition (MDtNBC). The MDtNBC is applied to an artificial boundary in CLS-FEM to ensure sound traveling outward and the solution's uniqueness. A hybrid acoustic stiffness is established to mitigate the dispersion error by combining the “overly stiff” FEM and the “overly soft” node-based smoothed FEM (NS-FEM) models. A key feature of CLS-FEM is its ability to significantly improve accuracy by appropriately softening acoustic stiffness without adding extra degrees of freedom. The performance of CLS-FEM is investigated numerically. Numerical examples are conducted to assess the characteristics of the approach. These simulations demonstrated that the proposed CLS-FEM significantly reduces the numerical dispersion error, achieving greater precision than both FEM and NS-FEM at large wave numbers. Hence, the developed method proves competitive for computing underwater noise.