A two-dimensional (2D) Reynolds-averaged Navier–Stokes (RANS) equations solver with k–ω turbulence closure is developed, employing immersed boundary (IB) technique on Cartesian grids. Generalized wall functions are introduced to enhance computational efficiency for problems with high Reynolds numbers. To address existing challenges in applying wall functions within IB methods, a novel, effective and easy-to-implement strategy is proposed. Another distinguishing feature of this turbulent-flow solver is that it employs the highly accurate immersed-boundary generalized harmonic polynomial cell (IB-GHPC) method to solve the Poisson equation for fluid pressure. The new solver is firstly validated by simulating channel flows on both hydraulically smooth and rough walls, achieving excellent agreement with benchmark experimental and numerical studies for various flow parameters including velocity, turbulent kinetic energy and shear stress. For channel flow simulations, our implementation of generalized wall functions using the proposed strategy results in a remarkable reduction of grid nodes by over 80%. Moreover, the solver is applied to simulate flow around both smooth and rough cylinders, producing promising results for drag, lift, and pressure coefficients. Our analysis demonstrates a robust performance of the developed solver in modeling turbulent flows based on Cartesian grids, offering a substantial improvement in computational efficiency for tackling problems involving large Reynolds numbers.
This paper presents ISOPE's 2020 comparative study on the interaction between focused waves and a fixed cylinder. The paper discusses the qualitative and quantitative comparisons between 20 different numerical solvers from various universities across the world for a fixed cylinder. The moving cylinder cases are reported in a companion paper as part B (Agarwal, Saincher, et al., 2021). The numerical solvers presented in this paper are the recent state of the art in the field, mostly developed in-house by various academic institutes. The majority of the participants used hybrid modeling (ie, a combination of potential flow and Navier–Stokes solvers). The qualitative comparisons based on the wave probe and pressure probe time histories and spectral components between laminar, turbulent, and potential flow solvers are presented in this paper. Furthermore, the quantitative error analyzes based on the overall relative error in peak and phase shifts in the wave probe and pressure probe of all the 20 different solvers are reported. The quantitative errors with respect to different spectral component energy levels (ie, in primary, sub-, and superharmonic regions) capturing capability are reported. Thus, the paper discusses the maximum, minimum, and median relative errors present in recent solvers as regards application to industrial problems rather than attempting to find the best solver. Furthermore, recommendations are drawn based on the analysis.