Development of an efficient incompressible flow solver on unstructured meshes

Abstract

A three-dimensional unstructured Incompressible flow solver has been developed to solve the Navier-Stokes equations based on the Pseudo-compressibility method. The code is applicable to steady Incompressible flow problems. A cell-centered finite volume method has been used in which all flow variables are defined at the centroid of the tetrahedrons (control volume) in an unstructured grid. The inviscid fluxes are computed using the Roe’s Flux Difference Splitting scheme, and higher-order spatial accuracy is attained by data reconstruction based on Taylor’s series expansion. The first derivatives of the viscous flux are evaluated by a linear reconstruction method. For time integration, an Implicit Jacobi/Gauss-Seidel method has been used to solve the resulting set of Governing equations. The one-equation turbulence model of Spalart and Allmaras has been used in the present code for calculating high Reynolds number flows. Wall function has been used to resolve the near solid-wall effects for turbulent flow problems to reduce the computational memory requirements. The inviscid flow solver has been validated using the NACA-0012 wing configuration and compared with the results of the well known Panel method results for $C_p$ distribution. The invisicd flow solver was then applied to the Sphere geometry and the $C_p$ distribution around the sphere was compared with available analytical data. The laminar flow solver was validated using the flat plate configuration and the results were compared with the blasius solution. The laminar flow solver was then applied to the sphere geometry and the comparisons were made for $C_D$ with experimental data. The turbulent flow solver was validated using the flat plate configuration. The flow solver was then applied to NACA-0012 configuration with different angle of attacks and the results were compared with the validated inhouse compressible flow solver for Ma=0.3 and with compressible experim...