Modified ghost fluid method on LBM with reduced spurious pressure oscillations for moving boundaries

A modified ghost fluid (MGF) method for reducing the spurious pressure oscillations in moving boundaries is proposed on the lattice Boltzmann method (LBM). The primary cause of these oscillations is the violation of the boundary geometric conservation law for sharp-interface immersed boundary. We introduce a simple weight strategy into GF method to strictly enforce geometric conservation. The weight strategy reduces the abrupt change of the distribution function on the boundary node when passing through the moving boundary. Some simulations are shown to test the validity of the method. The results illustrate that the modified method maintains the same validity as the GF and reduces the spurious pressure oscillations near the boundaries.

Effect of Geometric Conservation Law on Improving Spatial Accuracy for Finite Difference Schemes on Two-Dimensional Nonsmooth Grids

It is well known that grid discontinuities have significant impact on the performance of finite difference schemes (FDSs). The geometric conservation law (GCL) is very important for FDSs on reducing numerical oscillations and ensuring free-stream preservation in curvilinear coordinate system. It is not quite clear how GCL works in finite difference method and how GCL errors affect spatial discretization errors especially in nonsmooth grids. In this paper, a method is developed to analyze the impact of grid discontinuities on the GCL errors and spatial discretization errors. A violation of GCL cause GCL errors which depend on grid smoothness, grid metrics method and finite difference operators. As a result there are more source terms in spatial discretization errors. The analysis shows that the spatial discretization accuracy on non-sufficiently smooth grids is determined by the discontinuity order of grids and can approach one higher order by following GCL. For sufficiently smooth grids, the spatial discretization accuracy is determined by the order of FDSs and FDSs satisfying the GCL can obtain smaller spatial discretization errors. Numerical tests have been done by the second-order and fourth-order FDSs to verify the theoretical results.