Viscous effects are found to be very important in many engineering applications in marine hydrodynamics. It is well known that a proper viscous solver for the Navier-Stokes equations (NSEs) can achieve a better description for fluid-structure interaction problems especially in the flow at low Reynolds number. Even though the capacity of modern computers has been greatly increased, it is still challenging to solve NSEs numerically for many applications,&nbsp;mainly due to the high computational costs to achieve a required accuracy. Thus, it is of great importance to improve the efficiency and accuracy of Navier-Stokes equations solvers (Ferziger et al., 2002).The projection method is a very popular approach for solving NSEs where the pressure and velocities fields are decoupled (Chorin, 1968, Temam, 1969). One critical step in the projection method is to obtain an accurate solution for pressure Poisson equation, which is essential for the overall accuracy and efficiency of the Navier-Stokes equations.&nbsp;A promising method for solving the 2D Poisson equation called the generalized harmonic polynomial cell (GHPC) method, was developed and yields fourth-order accuracy in (Bardazzi et al.).&nbsp;GHPC method is a generalization of the 2D HPC method, which was originally proposed by Shao and Faltinsen as a general numerical method for the Laplace equation and the method has been successfully improved for 3D potential-flow problems (Shao and Faltinsen, 2012, 2014). Encouraged by the good performance of GHPC method, we have recently developed a new NSEs solver based on the GHPC method for Poisson equation and FDM for the convection-diffusion equations. The solver has been verified and validated on uniform grids with satisfactory results.The present paper will focus on the verification and validation of the solver on non-uniform grids. First, the performance of the GHPC method is verified on non-uniform meshes. The effect of grid-stretching ratio on the accuracy of the GHPC method will be examined, with the hope to suggest an optimal stretching strategy. Then, together with second-order FDMs for diffusion and advection terms, the verified GHPC method will be sued to solve the NSEs. Meanwhile, an immersed boundary method (Yang and Balaras, 2006)&nbsp;is used to study the fluid-structure-interaction problems. Problems of Taylor-Green vortex and flow around a smooth circular cylinder are studied to confirm the accuracy and efficiency of the viscous solver. The predictions show good agreements with the experimental and numerical results in the literature.Keywords:&nbsp;Navier-Stokes equations, generalized Harmonic Polynomial Cell method; non-uniform grids, stretching ratio

A 2d Navier-Stokes Equations Solver Based on Generalized Harmonic Polynomial Cell Method With Non-Uniform Grid

Paper Proceedings: https://asmedigitalcollection.asme.org/OMAE/OMAE2021/volume/85116

OMAE 2021

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