Heuristic acceleration correction algorithm for use in SPH computations in dynamic structural mechanics

Despite developments over the past 30 years, SPH and other mesh-free computational methods are not yet in general use as standard tools in dynamic structural mechanics. One possible reason for this is the use of features such as artificial viscosity, to stabilize the numerical computations, which can result in physically unreal phenomena. The effect of artificial viscosity in SPH computations is examined and a heuristic acceleration correction algorithm is proposed in this paper. The purpose is to improve the modelling of physically real effects and thereby make SPH a more attractive modelling option, particularly for structural impact problems.

The essence of the proposed method is to calculate the change in the acceleration due to the artificial viscosity term and then correct the computed acceleration by subtracting a kernel approximation of its artificial counterpart. The energy equation is also modified accordingly. By this means, the excessive dissipation is removed, while retaining the computational stabilizing effect of the artificial viscosity. For illustrative purposes, the proposed method is applied to several classical elastic and elastic–plastic impact problems and the results are compared with those available in the literature. In the process, the improved performance of the proposed algorithm vis-à-vis the standard SPH procedures is discussed as are the outstanding mathematical issues which require resolution to make the approach truly rigorous.