The weakly compressible SPH (WCSPH) method developed by Monaghan is widely applied for solving hydrodynamic problems. Although the conventional WCSPH method is a simple and frequently-used approach, it is generally affected by the poor accuracy and sometimes spurious oscillations which may lead to numerical instability. In order to dampen the pressure oscillation without introducing excessive dissipation, a modified Riemann solver with a low-dissipation limiter was proposed by Zhang et al.(i.e., Riemann-SPH). The present paper aims to integrate this low-dissipation Riemann solver into the finite particle method (FPM) proposed by Liu et al. to produce a Riemann-FPM which is expect to obtain better accuracy together with low dissipation.

The following table presents the spatial convergence rate of the Riemann-FPM for solving the unsteady Taylor-vortex flow at Re=100. It can be seen that by reducing the particle spacing, the accuracy of the solution is improved and second order convergence rate is achieved. Figure 1 shows the comparison of the pressure profile along the diagonal direction obtained by the proposed Riemann-FPM and the Riemann-SPH. It is clear that the proposed Riemann-FPM is superior to Riemann-SPH in producing smooth and accurate pressure field.