A hybrid implicit scheme for solving Navier-Stokes equations

A hybrid implicit scheme is developed in this study to solve 3D compressible Navier-Stokes equations on a hybrid unstructured mesh. An approximate evaluation technique for the residual term at a new time level is presented according to the analysis of the main physical mechanism introduced by the lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation-based backward Euler implicit method. The residual evaluation method is computationally inexpensive because it does not require flux calculations for every cell surface. The approximated new time residual can be obtained without considerable computational effort; thus, a point-implicit scheme with a multigrid property is designed to march a further time step after the previous LU-SGS-based backward Euler stage. This step leads to the principal ingredient of the presented two-stage hybrid implicit scheme. To investigate the convergence behavior and performance of the two-stage hybrid implicit scheme, 2D and 3D viscous flows around the NACA0012 airfoil, NHLP 2D multi-airfoil, and DLR-F6 wing-body-pylon-nacelle configuration are simulated by using different grid types. The convergence histories of the single LU-SGS-based backward Euler scheme and the presented two-stage hybrid implicit scheme are analyzed and compared for each test case. The test results show that the hybrid implicit scheme is more efficient and robust than the single-stage LU-SGS scheme. Copyright (C) 2015 John Wiley & Sons, Ltd.