Finite difference method

Abstract: A method is presented for adaptively solving hyperbolic PDEs. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids. The adaptability is performed automatically by thresholding the wavelet coefficients. Operations such as differentiation and multiplication are fast and simple due to the one-to-one correspondence between point values and wavelet coefficients in the interpolating basis. Treatment of boundary conditions is simplified in this sparse point representation (SPR). Numerical examples are presented for one- and two-dimensional problems. It is found that the proposed method outperforms a finite difference method on a uniform grid for certain problems in terms of flops.

Abstract: In this paper, the mesh-free least square-based finite difference (MLSFD) method is applied to numerically study the flow field around two circular cylinders arranged in side-by-side and tandem configurations. For each configuration, various geometrical arrangements are considered, in order to reveal the different flow regimes characterized by the gap between the two cylinders. In this work, the flow simulations are carried out in the low Reynolds number range, that is, Re = 100 and 200. Instantaneous vorticity contours and streamlines around the two cylinders are used as the visualization aids. Some flow parameters such as Strouhal number, drag and lift coefficients calculated from the solution are provided and quantitatively compared with those provided by other researchers.