SPH hydrocodes can be stabilized with shape-shifting

Grid free methods, such as SPH (Smoothed Particle Hydrodynamics), may, eventually, be more efficacious in their representations of material dynamics than the standard fixed grid methods. However, standard SPH (with stress = σ and interpolation weight = W) has instabilities when σW″ < 0 in both compression (σ > 0) and in tension (σ < 0). Conservative smoothing can control the SPH instabilities, but it may smooth out more of the short wave length structure than desired. SPH can also be stabilized by shifting the shape of W to change the sign of W″.