Accelerate the numerical convergence of incompressible flows: Novel preconditioned characteristic boundary conditions

Abstract

For the first time, the locally power-law preconditioning method (LPLPM) is used to formulate the preconditioned characteristic boundary conditions (CBCs). Then, it is implemented to solve the numerical modeling of unsteady and steady flows from viscous to turbulent regimes. The compatibility equations and Riemann invariants are mathematically derived and then utilized to the incompressible flow solvers as suitable boundary conditions. This method discretizes time derivative and governing equations' space terms by applying the four-stage, fourth-order Runge–Kutta method, and a finite volume, respectively. The preconditioning matrix in the LPLPM is automatically derived by local velocity sensors through a power-law formulation. The baseline k−ω is applied as an appropriate turbulence model. Several test cases are conducted around airfoils of Office National d'Etudes et de Recherches Aerospatiales, NACA0012 (National Advisory Committee for Aeronautics), and S809 at varied angles of attack of 0–20 and Reynolds numbers of 500 to 5.25 × 106 to examine the effectiveness and accuracy of the LPLPM employing preconditioned CBCs. A sensitivity analysis is also performed to examine how numerical parameters affect the simulation. The results show that using preconditioned CBCs in conjunction with LPLPM at the artificial boundary is precise, reliable, and computationally efficient in simulating viscous/turbulent flows. Furthermore, it is also concluded that the present approach considerably improves the convergence speed contrasted to the simplified boundary conditions.