Solving time-dependent PDEs using the material point method, a case study from gas dynamics

The Material Point Method (MPM) developed by Sulsky and colleagues is currently being used to solve many challenging problems involving large deformations and/or fragmentations with some success. In order to understand the properties of this method, an analysis of the considerable computational properties of MPM is undertaken in the context of model problems from gas dynamics. The MPM method in the form used here is shown both theoretically and computationally to have first order accuracy for a standard gas dynamics test problem. Copyright c ©2008 John Wiley & Sons, Ltd. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2008; 00:1–23 Prepared using fldauth.cls [Version: 2002/09/18 v1.01] Solving Time-Dependent PDEs using the Material Point Method, A Case Study from Gas Dynamics. † L.T.Tran 1,∗, J.Kim 1 M. Berzins1,2 1 School of Computing, University of Utah, Salt Lake City, Utah 2 SCI Institute, University of Utah, USA. SUMMARY The Material Point Method (MPM) developed by Sulsky and colleagues is currently being used to solve many challenging problems involving large deformations and/or fragementations with some success. In order to understand the properties of this method, an analysis of the considerable computational properties of MPM is undertaken in the context of model problems from gas dynamics. The MPM method in the form used here is shown both theoretically and computationally to have first order accuracy for a standard gas dynamics test problem. Copyright c © 2008 John Wiley & Sons, Ltd. key words: MPM Particle method, Error Estimates