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Particle shifting techniques (PST) have been used to improve the accuracy ofthe Smoothed Particle Hydrodynamics (SPH) method. Shifting ensures that theparticles are distributed homogeneously in space. This may be performed bymoving the particles using a transport velocity. In this paper, we propose anextension to the class of Transport Velocity Formulation (TVF) methods. Wederive the equations in a consistent manner and show that there are additionalterms that significantly improve the accuracy of the method. In particular, weapply this to the Entropically Damped Artificial Compressibility SPH method. Weidentify the free-surface particles and their normals using a simple approachand thereby adapt the method for free-surface problems. We show how the newmethod can be applied to the problem of elastic dynamics. We consider a suiteof benchmark problems involving both fluid and solid mechanics to demonstratethe accuracy and applicability of the method. The implementation is opensource, and the manuscript is fully reproducible.

A corrected transport-velocity formulation for fluid and structural mechanics with SPH