A transport-velocity formulation for smoothed particle hydrodynamics

The standard weakly-compressible SPH method suffers from particle clumping and void regions for high Reynolds number flows and when negative pressures occur in the flow. As a remedy, a new algorithm is proposed that combines the homogenization of the particle configuration by a background pressure while at the same time reduces artificial numerical dissipation. The transport or advection velocity of particles is modified and an effective stress term occurs in the momentum balance that accounts for the difference between advection velocity times particle density and actual particle momentum. The present formulation can be applied for internal flows where the density summation is applicable. A wide range of test cases demonstrates unprecedented accuracy and stability of the proposed modification even at previously infeasible conditions.