Analysis/application of stabilization by the over-integration technique in CBS-SEM for incompressible flow

Abstract

When the characteristic-based split (CBS) scheme is combined with spectral element method (SEM), high-order nonlinear terms in CBS scheme produce non-negligible aliasing error, which causes severe stability problems. In this paper, a stabilized framework based on CBS-SEM for incompressible flow simulation is established with stabilization by over-integration. The introduced over-integration addresses the aliasing-driven instability by approximating nonlinear terms with higher-order interpolations. A numerical experiment is presented to assess the performance of the stabilized framework in terms of the stability range, solution quality, and computational efficiency. The main conclusions are as follows: (1) Over-integration effectively extends the range of stability for CBS-SEM, where the increase in low-order interpolations is more significant. (2) For extremely under-resolved problems, two types of instabilities, including instability caused by the limitation of CFL condition and instability triggered by aliasing error, are observed in the numerical experiment. The stabilized framework is verified to be effective in handling both types of instability. (3) The order of over-integration only slightly affects the stability, but it markedly improves the capture of complex flow structure for high-order interpolations. In addition, a numerical investigation on incompressible flow past an airfoil is performed to further demonstrate the effectiveness of the framework.