This paper proposes a generalization of the explicit central-difference time integration scheme, using a time step variable not only in time but also in space. The solution at each element/node is advanced in time following local rather than global stability limitations. This allows substantial saving of computer time in realistic applications with non-uniform meshes, especially in multi-field problems like fluid¿structure interactions. A binary scheme in space is used: time steps are not completely arbitrary, but stay in a constant ratio of two when passing from one partition level to the next one. This choice greatly facilitates implementation (via an integer-based logic), ensures inherent synchronization and avoids any interpolations, necessary in other partitioning schemes in the literature, but which may reduce numerical stability. The mesh partition is automatically built up and continuously updated by simple spatial adjacency considerations. The resulting algorithm deals automatically with large variations in time of stability limits. The paper introduces the core spatial partitioning technique in the Lagrangian formulation. Some academic numerical examples allow a detailed comparison with the standard, spatially uniform algorithm. A final more realistic example shows the application of partitioning in simulations with arbitrary Lagrangian Eulerian formulation and fully-coupled boundary conditions (fluid¿structure interaction).

CASADEI Folco;  HALLEUX Jean-Pierre; 

2009-06-11

JOHN WILEY & SONS LTD

JRC34676

0029-5981,   

https://publications.jrc.ec.europa.eu/repository/handle/JRC34676,   

10.1002/nme.2533,