Ship hydrodynamics computations with the CIP method based on adaptive Soroban grids

The constrained interpolation profile/cubic interpolated pseudo-particle (CIP) combined unified procedure (CCUP) method (J. Phys. Soc. Jpn. 1991; 60:2105-2108), which is based on the CIP method (J Comput. Phys. 1985; 61:261-268; J. Comput. Phys. 1987; 70:355-372; Comput. Phys. Commun. 1991; 66:219-232; J. Comput. Phys. 2001; 169:556-593) and the adaptive Soroban grid technique (J. Comput. Phys. 2004; 194:55-77) were combined in (Comput. Mech. 2006; published online) for computation of 3D fluid-object and fluid-structure interactions in the presence of free surfaces and fluid-fluid interfaces. Although the grid system is unstructured, it still has a very simple data structure and this facilitates computational efficiency. Despite the unstructured and collocated features of the grid, the method maintains high-order accuracy and computational robustness. Furthermore, the meshless feature of the combined technique brings freedom from mesh moving and distortion issues. In this paper, the combined technique is extended to ship hydrodynamics computations. We introduce a new way of computing the advective terms to increase the efficiency in that part of the computations. This is essential in ship hydrodynamics computations where the level of grid refinement needed near the ship surface and at the free surface results in very large grid sizes. The test cases presented are a test computation with a wave-making wedge and simulation of the hydrodynamics of a container ship.

[1]  Tayfun E. Tezduyar,et al.  Fluid-structure interactions of a parachute crossing the far wake of an aircraft , 2001 .

[2]  Takashi Yabe,et al.  A universal solver for hyperbolic equations by cubic-polynomial interpolation I. One-dimensional solver , 1991 .

[3]  T. Tezduyar.  Computation of moving boundaries and interfaces and stabilization parameters , 2003 .

[4]  D. Dinkler,et al.  A monolithic approach to fluid–structure interaction using space–time finite elements , 2004 .

[5]  D. Peric,et al.  A computational framework for fluid–structure interaction: Finite element formulation and applications , 2006 .

[6]  T. Yabe,et al.  The constrained interpolation profile method for multiphase analysis , 2001 .

[7]  K. Tanizawa.  A Nonlinear Simulation Method of 3-D Body Motions in Waves (1st Report) , 1995 .

[8]  W. Wall,et al.  A Solution for the Incompressibility Dilemma in Partitioned Fluid–Structure Interaction with Pure Dirichlet Fluid Domains , 2006 .

[9]  Arif Masud,et al.  A multiscale finite element method for the incompressible Navier-Stokes equations , 2006 .

[10]  H. Takewaki,et al.  The cubic-interpolated Pseudo particle (cip) method: application to nonlinear and multi-dimensional hyperbolic equations , 1987 .

[11]  Tayfun E. Tezduyar,et al.  Finite element methods for flow problems with moving boundaries and interfaces , 2001 .

[12]  Kenji Takizawa,et al.  Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme , 2004 .

[13]  Tayfun E. Tezduyar,et al.  Simulation of multiple spheres falling in a liquid-filled tube , 1996 .

[14]  Tayfun E. Tezduyar,et al.  PARALLEL FINITE ELEMENT SIMULATION OF 3D INCOMPRESSIBLE FLOWS: FLUID-STRUCTURE INTERACTIONS , 1995 .

[15]  Roger Ohayon,et al.  Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-sloshing systems , 2001 .

[16]  Takashi Yabe,et al.  Cubic interpolated pseudo-particle method (CIP) for solving hyperbolic-type equations , 1985 .

[17]  Arif Masud,et al.  Effects of Mesh Motion on the Stability and Convergence of ALE Based Formulations for Moving Boundary Flows , 2006 .

[18]  Arif Masud,et al.  A Multiscale/stabilized Formulation of the Incompressible Navier–Stokes Equations for Moving Boundary Flows and Fluid–structure Interaction , 2006 .

[19]  Takashi Yabe,et al.  Unified Numerical Procedure for Compressible and Incompressible Fluid , 1991 .

[20]  Arif Masud,et al.  An adaptive mesh rezoning scheme for moving boundary flows and fluid-structure interaction , 2007 .

[21]  René de Borst,et al.  On the Nonnormality of Subiteration for a Fluid-Structure-Interaction Problem , 2005, SIAM J. Sci. Comput..

[22]  Toshiaki Hisada,et al.  Fluid–structure interaction analysis of the two-dimensional flag-in-wind problem by an interface-tracking ALE finite element method , 2007 .

[23]  Tayfun E. Tezduyar,et al.  Computation of flow problems with the Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) , 2007 .

[24]  Tayfun E. Tezduyar,et al.  Space-time finite element techniques for computation of fluid-structure interactions , 2005 .

[25]  S. Mittal,et al.  A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. II: Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders , 1992 .

[26]  van Eh Harald Brummelen,et al.  The relevance of conservation for stability and accuracy of numerical methods for fluid?structure interaction , 2003 .

[27]  Tayfan E. Tezduyar,et al.  Stabilized Finite Element Formulations for Incompressible Flow Computations , 1991 .

[28]  T. Tezduyar,et al.  A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. I: The concept and the preliminary numerical tests , 1992 .