A finite particle method based on a Riemann solver for modeling incompressible flows

The weakly compressible SPH (WCSPH) method has been widely used for solving hydrodynamic problems, in which the fluid is assumed to be weakly compressible through limiting the density deviation to a small value. Despite its simplicity and robustness in implementation, the WCSPH method is generally hindered by its poor accuracy and spurious oscillations in the pressure field which may lead to numerical instability. In order to dampen the spurious oscillations without introducing excessive dissipation, a Roe-type approximate Riemann solver with a low-dissipation limiter was proposed and applied to the WCSPH method by Zhang et al. (2017). The present paper aims to extend this low-dissipation Riemann solver to the finite particle method (FPM), which can be referred to an enhanced or modified version of the conventional SPH method, for reducing spurious pressure oscillations and meanwhile achieving higher order of accuracy. Numerical results demonstrate that the Riemann solver based FPM is effective in modeling incompressible flows and it produces a more accurate flow field than the conventional WCSPH and Riemann solver based WCSPH methods.