A fully implicit particle-in-cell method for granular flows
- Sharen J.
- Jeremiah U.
A wide variety of numerical models have been used to capture the complexities of granular flow. Examples include Monte Carlo models, lattice gas models and numerical models to resolve the grains. The latter is the subject of this paper. In particular, an implicit formulation of the material point method (MPM) is considered in the modeling of granular materials. MPM combines a Lagrangian treatment, using material points, with an Eulerian grid. These material points describe the grain dynamics, they resolve edges and allow history dependent effects to be recorded. The Eulerian grid allows for efficient computation of interactions between grains. Contacts between grains are computed with a model based on the immersed boundary method; interpenetration is prevented but grain separation, sliding and bonding are allowed. Previous versions of the MPM algorithm advance the solution in time using a leapfrog algorithm. These work well for relatively high strain rates but implicit methods have the potential to be more robust, stable and efficient for low strain rate calculations. In this paper, a Newton-Krylov (NK) algorithm is applied to the solution of the implicit MPM equations. The implementation is matrix-free, requiring only the evaluation of the residual error at each iterative step - ideal in the solution of the non-linear and non-analytic implicit MPM formulation. In this paper, the granular flow model is presented and the implicit MPM formulation described. Next, the implementation of the Newton-Krylov technique is discussed and the results of numerical experiments for a single grain and an assembly of compressed grains presented. An implicit-in-time method for granular materials is described. The method combines the Material Point Method (MPM), and a Newton-Krylov equation solver to give improved energy conservation and stabilization.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 975653
- Report Number(s):
- LA-UR-01-4102; TRN: US201008%%244
- Resource Relation:
- Conference: Submitted to: 6th U.S. National Congress on Computational Mechanics Conference, Dearborn, Michigan, August 1-3, 2001
- Country of Publication:
- United States
- Language:
- English
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