Preconditioning methods for compressible flow CFD codes: Revisited

Abstract

The present article aims to implement and investigate a different preconditioning method based in a three-dimensional in-house compressible CFD code that ensures the robustness and numerical stability to determine the flowfield considering low Mach number flow. The present preconditioning method involve two different methodologies developed by references [8, 32]. The CFD solver was developed to calculate the Euler and Navier-Stokes equations, numerically, for steady-state regime based on the cell-centered finite volume method (FVM) using Reynolds Averaged Navier-Stokes equations (RANS). The centered second-order scheme was used for the discretization of convective terms from momentum equations. The explicit second-order five-step Runge-Kutta scheme was employed for the time-marching procedure, using an implicit residual smoothing technique to enhance the numerical stability. A local preconditioning method was implemented due to its robustness in predicting low Mach number flows in a compressible CFD code environment. However, for low Mach number flows, near stagnation points, numerical perturbations were amplified generating a stiffness in the convergence rate, which provided an inaccurate solution and numerical stability degradation. Aiming to improve the preconditioning robustness, a flux function and a new limiter were applied to operate with the preconditioning technique based on a pressure sensor. Those corrections re-scale the eigenvectors and ensure the locality of the algorithm, which improves the numerical stability and guarantees the convergence for low-speed flows. The inviscid flow over a NACA 0012 airfoil for compressible and incompressible cases shown accurate and robust solutions. For a viscous flow over a flat plate case in the compressible and incompressible cases, the preconditioning technique purposed in this work supplied good numerical solution in agreement with the analytical solution.