A Simple Verification Test for Nonlinear Flow Calculations Around a Ship Hull Steadily Advancing in Calm Water

Simple analytical relations that can readily be applied to verify a critical aspect of numerical predictions of fully nonlinear free-surface flows around ship hulls steadily advancing in calm water are given. The relations do not involve the flow field equations; that is, they are only based on the boundary conditions at the ship hull surface and at the free surface. These boundary conditions have a predominant influence on free-surface flows around advancing ship hulls. The analytical relations are exact for inviscid flows, and can be applied to numerical methods that solve either the Laplace equation (potential-flow methods) or the Euler flow equations (CFD Euler-flow methods). They provide a simple test to verify if numerical predictions given by nonlinear potential-flow or Euler-flow methods correctly satisfy the hull-surface and free-surface boundary conditions along the contact curve between the hull surface and the free surface. The relations might also be used to verify CFD methods that solve the RANS equations if they are applied at the edge of the viscous boundary layer. The analytical test can identify an inconsistency, which might point to a "method issue" related to a feature of a numerical method (e.g., a numerical-differentiation scheme) or an "implementation issue" in the implementation of the method (e.g., a poor discretization). For purposes of illustration, the test is applied to predictions of flows around the Wigley parabolic hull given by two CFD methods that solve the Euler equations with fully nonlinear boundary conditions at the free surface. This illustrative example demonstrates that the test can indeed be useful to identify numerical inaccuracies. The analytical relations can also be used to determine experimental values of the flow velocity at a ship wave profile that correspond to measurements of the wave profile.