Toward Wall Modeling in Cartesian Grid Solver Using Overset Grid Technique for Ship Hydrodynamics

A Cartesian grid solver is coupled with an orthogonal curvilinear grid solver using overset grid interpolation and a coupled pressure Poisson solver. It aims at resolving the boundary layer on the body surface effectively. SUGGAR code, an overset grid assembly program, provides overset grid information of a Cartesian background grid and a thin orthogonal body-fitted grid to resolve the boundary layer on the surface. The overset grid information is used to interpolate velocity, pressure, turbulence quantities, and level set function. A coupled pressure Poisson equation is solved using PETSc. The coupled curvilinear/Cartesian grid solver has been applied to two-phase turbulent flows past a circular cylinder and has shown good agreement with the experimental data and the LES results in the literature. The solver is being applied to a free surface flow around Wigley’s parabolic hull form at Re = 3.4×10 6 and Fr = 0.25. The numerical results are promising compared to an experimental result of wave elevations at the same Fr. MOTIVATION AND OBJECTIVE Computational fluid dynamics (CFD) solvers with high fidelity are required to perform accurate simulations of turbulent flows. Such CFD solvers should include high-order numerical schemes, accurate turbulence modeling, and good scalability of high performance computing (HPC). Simplicity of generating computational grids is also important for complex geometries such as those observed in ship hydrodynamics. Generation of a body-fitted structured grid around the complex geometry surface is difficult, and mesh quality, namely mesh orthogonality and mesh smoothness, often becomes an issue. On the other hand, unstructured grids show greater flexibility to geometry shapes and are easier to generate around the complex surfaces than the structured grids. However, implementation of high-order numerical schemes and accurate turbulence models such as large eddy simulation (LES) is difficult to the unstructured grid solvers. CFD solvers using a Cartesian grid with an immersed boundary method (IBM) involve extremely easy grid generation and allow implementation of high-order numerical schemes easily. Also, HPC scalability of the Cartesian grid solvers is better than that of the curvilinear structured grid solvers. Because of these features, the Cartesian grid solvers with IBM are well suited for accurate numerical simulations of turbulent flows, such as LES (Yang and Stern, 2009). However, the Cartesian grid solvers require very large grids to adequately resolve boundary layers at high Reynolds numbers. Adaptive local grid refinement near the solid wall can lead to reduction of the grid size (Iaccarino et al., 2004), but still the near-wall grid resolution is very expensive. Moreover, the fine near-wall resolutions require very small time steps to simulate unsteady or developing flows accurately. Thus, wall layer (WL) modeling is an important issue for the Cartesian grid solvers to achieve appropriate resolution of the viscous flows around the solid surfaces. A WL modeling approach proposed by Yang and Stern (2009) is a coupled curvilinear/Cartesian grid method. In this method, curvilinear structured grids are used to resolve the boundary layers on the solid surfaces and Cartesian grids to compute the flow regions out of the boundary layers. Different CFD solvers are applied to the body-fitted curvilinear grids and the Cartesian background grids. Those solvers can be coupled using an overset grid method. The Structured, Unstructured, and Generalized overset Grid AssembleR (SUGGAR) code was developed as an overset grid assembly program by Noack (2005). The SUGGAR code can create a single composite grid from multiple overlapping structured, unstructured, and/or general polyhedral grids for both node-centered and cell-centered flow solvers. It has been incorporated into existing flow solvers, and the solvers with the overset grid capability have been validated for several problems including static or dynamic objects (Pandya et al., 2005;