Stability of DPD and SPH
It is shown that DPD (Dual Particle Dynamics) and SPH (Smoothed Particle Hydrodynamics) are conditionally stable for Eulerian kernels and linear fields. This result is important because it is highly desirable to move and change neighbors where the material deformation is large. For higher dimensions (than 1D), stability for general neighborhoods is shown to require a two-step update, such a predictor-corrector. Co-locational methods (all field variables calculated on every particle) benefit from the completeness property also. We show that SPH with corrected derivatives is conditionally stable. Linear completeness of interpolations is shown to assert itself as a powerful ally with respect to stability as well as accuracy.
KeywordsSmooth Particle Hydrodynamic Background Field Move Little Square Stress Point Motion Point
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