Efficient Formulations for Quasi-Steady Processes Simulations: Multi-Mesh Method, Arbitrary Lagrangian or Eulerian Formulation and Free Surface Algorithms

摘要

Numerical simulation of forming processes like rolling may require prohibitive computational times. Calculations can be speeded-up by different recently developed numerical methods. If the process can be considered as steady, then the steady-state can be directly computed using an iterative approach based on free surface corrections: the domain shape is computed alternately with the resolution of mechanical equations. In the frame of 3D unstructured meshes, complex shapes and parallel calculations, it is proposed to use a global formulation based on a least square functional with an upwind shift for taking into account contact conditions. It is shown to converge from any initial shape of the domain. If the process is only quasi-steady, then the computational cost can be reduced by considering a smaller part of the domain, which is made possible by an Arbitrary Eulerian or Lagrangian formulation. A general formulation is developed, which applies to a wide range of forming processes. In rolling, the observed computational cost reduction varies between 2 and 7 in parallel. If an incremental Lagrangian approach is inescapable, then the multi-mesh method makes it possible to reduce the computational cost by using several meshes on the same domain. Each mesh is optimal for a particular physic of the domain. This approach provides speed-ups up to 10 in a parallel computing environment.