A potential flow model with viscous dissipation based on a modified boundary element method

Abstract

Conventional potential flow models are known to exaggerate predictions in water wave resonance problems, attributed to the inviscid fluid assumption in the potential theory. In this paper, we present a modified potential flow model incorporating the viscous dissipation effect. We introduce some ’dissipative surfaces’ inside the fluid domain which are defined such that the normal velocity through these surfaces remains continuous but a pressure drop occurs across them, representing physically the viscous dissipation. In formulating the boundary value problem using Green theorem by a boundary element method (BEM), modified boundary integral equations are deduced to include the integral over the dissipative surfaces. We apply this model to three cases where overestimation is reported using classical potential models: gap resonance, monocolumn moonpool resonance and tuned wave surge converter. Numerical results show that the dissipative surface is effective to dampen the responses at resonance. Validation is carried out by comparisons against either experimental data or analytical solutions. The spikes in the response amplitude operators (RAOs) produced from the non-dissipative model are removed with inclusion of dissipation. Importantly, the proposed model with dissipation effect favorably retains the same level of computational efficiency as with the classical potential flow model.