A new high-order particle method for solving high Reynolds number incompressible flows

Abstract

In this study, a new high-order particle method is proposed to solve the incompressible Navier–Stokes equations. The proposed method combines the advantages of particle and mesh methods to approximate the total and the spatial derivative terms under the Lagrangian and the Eulerian frameworks. Our aim is to avoid convective instability and increase solution accuracy at the same time. Data transfer from Lagrangian particles to Eulerian grids is realized by moving least squares interpolation. In contrast to the previously proposed method, there is no need to interpolate diffusion terms from Eulerian grids to Lagrangian particles. Therefore, the accuracy of the present solution will not be deteriorated by interpolation error. Additionally, no extra work is required to manage particles for searching procedure. Because no convection term needs to be discretized by upwinding schemes, false diffusion and dispersion errors will not be introduced, thereby increasing the solution accuracy. To verify the proposed particle method, several benchmark problems are solved to show that the present simulation is more stable, accurate, and efficient. The proposed particle method renders fourth- and second-order accurate solutions in space for velocity and pressure, respectively.

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