An Eulerian SPH method with WENO reconstruction for compressible and incompressible flows

While Eulerian smoothed particle hydrodynamics (SPH) method has received increasing attention in scientific and industrial communities owing to its high spatial accuracy, it exhibits excessive numerical dissipation due to the fact that the flux is derived in particle pair pattern. In this paper, we adopt a one-dimensional weighted essentially non-oscillatory (WENO) reconstruction to reduce the numerical dissipation and improve the overall accuracy particularly in capturing the contact discontinuity. The underlying principle is to construct a 4-point stencil along the interacting line of each particle pair and then the WENO scheme is applied to reconstruct the initial states of the Riemann problem which determines the flow flux. A set of benchmark tests for both compressible and incompressible flows are studied to investigate the accuracy, robustness and versatility of the proposed Eulerian SPH method with the WENO reconstruction (ESPH-WENO).