Energy balance in quasi-Lagrangian Riemann-based SPH schemes

The Smoothed Particle Hydrodynamics (SPH) method suffers from the presence of irregular particle distributions inherent in its Lagrangian nature. A way to circumvent this problem is consider a quasi-Lagrangian SPH scheme and use Shifting Technique (PST). In framework, we include an approximate Riemann solver represent interaction obtain two different Riemann-based schemes: one mass-constant model whereas other derived ALE formalism. These schemes are examined validated by focusing on their energy balance. particular, contribution provided terms associated PST studied both theoretical numerical point view. consistency diffusive properties these investigated test cases involving confined free-surface flows. Albeit investigation performed for specific PST, proposed methodology can be easily extended formulations.