Computation of steady and unsteady flows with a free surface around the Wigley hull

Abstract

The previously reported Modified Artificial Compressibility approach to solve unsteady, two dimensional free surface flows using Euler equations has been extended to solve unsteady, three dimensional free surface flows using Navier-Stokes equations. This approach provides a natural way of incorporating the body force term due to gravity in a higher order scheme. The numerical scheme, UNCLE, is a finite volume, implicit, upwind scheme that uses the Roe variables for computing the fluxes at the cell interfaces and the MUSCL approach for obtaining higher order corrections. The flux Jacobians are obtained using numerical (Frechet) differentiation. The free surface is tracked using the moving grid approach which results in an accurate way of applying the boundary conditions preventing leaks through the free surface. Both Euler and Navier-Stokes computations have been performed. Turbulence is accounted using the Baldwin-Lomax model. This scheme is used to study steady and unsteady flows around a Wigley hull. Steady flow is studied by keeping the body stationary in a uniform flow. Unsteady aspect of the flow is induced by heaving the body using a sinusoidal function. The amplitude of heaving was 0.4 times the draft. Comparisons have been made with available experimental results for the case of the steady motion and the agreement is quite good. No data is available to make comparisons with the unsteady motion.