High-accurate SPH method with Multidimensional Optimal Order Detection limiting

•A new high-accurate SPH method based on Riemann solvers is presented.•MLS approximations are used for the reconstruction step in the Riemann solver.•The stability of the scheme is achieved by the a posteriori MOOD paradigm.•Important gains in accuracy are obtained for problems involving non-smooth flows.

We present a new high-accurate, stable and low-dissipative Smooth Particle Hydrodynamics (SPH) method based on Riemann solvers. The method derives from the SPH-ALE formulation first proposed by Vila and Ben Moussa. Moving Least Squares approximations are used for the reconstruction of the variables and the computation of Taylor expansions. The stability of the scheme is achieved by the a posteriori Multi-dimensional Optimal Order Detection (MOOD) paradigm. Such a procedure enables to provide genuine gains in accuracy both for one- and two-dimensional problems involving non-smooth flows when compared to classical SPH methods.