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

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.

[1]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[2]  C. W. Hirt,et al.  Free-surface stress conditions for incompressible-flow calculations☆ , 1968 .

[3]  Sukumar Chakravarthy,et al.  Unified formulation for incompressible flows , 1989 .

[4]  M. L. Stokes,et al.  EAGLEView: A surface and grid generation program and its data management , 1992 .

[5]  L. K. Taylor,et al.  Numerical solution of the two-dimensional time-dependent incompressible Euler equations , 1994 .

[6]  M. Ikehata,et al.  Computation of free surface waves around an arbitrary body by a Navier‐Stokes solver using the psuedocompressibility technique , 1994 .

[7]  H. C. Yee,et al.  A class of high resolution explicit and implicit shock-capturing methods , 1989 .

[8]  Lafayette K. Taylor,et al.  A time accurate calculation procedure for flows with a free surface using a modified artificial compressibility formulation , 1994 .

[9]  Z. Warsi.  Fluid dynamics: theoretical and computational approaches , 1993 .

[10]  L. K. Taylor,et al.  Unsteady three-dimensional incompressible algorithm based on artificial compressibility , 1991 .

[11]  Hideaki Miyata,et al.  Finite-difference simulation of nonlinear ship waves , 1985 .

[12]  Hideaki Miyata,et al.  Numerical Study on a Viscous Flow with Free-Surface Waves About a Ship in Steady Straight Course by a Finite-Volume Method , 1992 .

[13]  Joe F. Thompson,et al.  Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies , 1974 .

[14]  D. Whitfield,et al.  Discretized Newton-relaxation solution of high resolution flux-difference split schemes , 1991 .

[15]  Frederick Stern,et al.  An interactive approach for calculating ship boundary layers and wakes for nonzero Froude number , 1992 .

[16]  A. Chorin.  A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .

[17]  J. F. Thompson.  Numerical solution of flow problems using body-fitted coordinate systems , 1978 .

[18]  D A Caughey,et al.  Frontiers of computational fluid dynamics 1994 , 1994 .

[19]  Mike J. Baines.  Introduction to “Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes” , 1997 .

[20]  Hideaki Miyata,et al.  Difference solution of a viscous flow with free-surface wave about an advancing ship , 1987 .

[21]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[22]  H. Lomax,et al.  Thin-layer approximation and algebraic model for separated turbulent flows , 1978 .

[23]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[24]  Z. U. A. Warsi.  A synopsis of elliptic PDE models for grid generation , 1987 .

[25]  Antony Jameson,et al.  Fast multigrid method for solving incompressible hydrodynamic problems with free surfaces , 1993 .