High-order Eulerian SPH scheme through W/TENO reconstruction based on primitive variables for simulating incompressible flows

The present work targets a high-order SPH scheme for simulating incompressible flows. To achieve this, typical spatial reconstructions, piecewise constant approximation, MUSCL, WENO and TENO techniques are employed in the Riemann-SPH formulation. These reconstructions are based on primitive variables rather than numerical fluxes, and the advection term is not altered. Therefore, the polynomial coefficients and the optimal weights in the W/TENO reconstruction are corrected to adapt this system. The accuracy of SPH is improved by W/TENO reconstruction up to 4th and 5th order in the Eulerian framework, respectively. The performances in the Lagrangian, ALE and Eulerian frameworks, and of different reconstructions are also compared. TENO-SPH can obtain comparable results with half (or even lower) of the particle resolution as compared to previous SPH versions. Moreover, the constraint of mass change related to the volume conservation and pressure instabilities is investigated in the Eulerian framework.