A targeted essentially non-oscillatory (TENO) SPH method and its applications in hydrodynamics

In this paper, we propose a targeted essentially non-oscillatory (TENO) SPH scheme. In this scheme, a 5 point stencil consisting of 3 candidate sub-stencils is adopted to implement the TENO reconstruction as originally proposed in the mesh-based methods. In the original TENO reconstruction, these five points are fixed and equidistant. However, it is difficult for SPH to determine these five points due to the random particle distribution. To remedy this issue, for two interacting particles, we first consider them as two existing stencil points. Then, for the other three points, we search for the closest particles to their exact positions. Subsequently, considering the gradient of these particles, we can finally obtain the values of these target points. Afterwards, the primitive values of points are reconstructed by TENO reconstruction where the polynomial interpolations are modified. Numerical results show that the proposed TENO-SPH scheme can be applied to reproduce some compressible flows involving shocks and small-scale structures, some incompressible vortex flows and free surface flows with superior accuracy.

Automated summary

This paper proposes a targeted essentially non-oscillatory (TENO) SPH scheme, which can be applied to reproduce compressible flows with shocks and small-scale structures, incompressible vortex flows, and free surface flows. The TENO reconstruction is implemented by modifying polynomial interpolations in SPH.