A consistent continuous particle reordering in weakly-compressible SPH through an ALE formalism

Due to its Lagrangian property, the SPH method may exhibit convergence limitations resulting from the presence of anisotropic particle structures that follows the physical defor- mations of the media to be modeled. Therefore, various papers addressed this problem, and proposed solutions dedicated to the disruption of these structures. However, these methods usually act directly on the transport velocity without taking care of the possibly wrong effects of such corrections on the stability and consistency of the numerical scheme. In this paper, the use of an Arbitrary Lagrangian Eulerian (ALE) formalism dedicated to the weakly-compressible SPH method is proposed as a solution to disrupt these particle structures while preserving some favorable numerical properties of the resulting scheme. Applications to academic test cases are proposed in order to emphasize the interest of the proposed scheme.