Binary spatial partitioning of the central‐difference time integration scheme for explicit fast transient dynamics

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). Copyright © 2008 John Wiley & Sons, Ltd.

[1]  W. Daniel.  Analysis and implementation of a new constant acceleration subcycling algorithm , 1997 .

[2]  Alain Combescure,et al.  Automatic energy conserving space–time refinement for linear dynamic structural problems , 2005 .

[3]  Alain Combescure,et al.  Multi-time-step explicit–implicit method for non-linear structural dynamics , 2001 .

[4]  Ted Belytschko,et al.  Mixed methods for time integration , 1979 .

[5]  Wing Kam Liu,et al.  Stability of multi-time step partitioned integrators for first-order finite element systems , 1985 .

[6]  Shripad Thite,et al.  An h-adaptive spacetime-discontinuous Galerkin method for linear elastodynamics , 2006 .

[7]  J. P. Halleux,et al.  Transient fluid–structure interaction algorithms for large industrial applications , 2001 .

[8]  F. Casadei,et al.  An algorithm for permanent fluid-structure interaction in explicit transient dynamics , 1995 .

[9]  Alain Combescure,et al.  A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis , 2002 .

[10]  Antonio Huerta,et al.  New ALE applications in non-linear fast-transient solid dynamics , 1994 .

[11]  Alain Combescure,et al.  An approach to the connection between subdomains with non‐matching meshes for transient mechanical analysis , 2002 .

[12]  Ted Belytschko,et al.  Partitioned and Adaptive Algorithms for Explicit Time Integration , 1981 .

[13]  W. Daniel.  A study of the stability of subcycling algorithms in structural dynamics , 1998 .

[14]  A. Prakash,et al.  A FETI‐based multi‐time‐step coupling method for Newmark schemes in structural dynamics , 2004 .

[15]  Vincent Faucher,et al.  Local modal reduction in explicit dynamics with domain decomposition. Part 2: specific interface treatment when modal subdomains are involved , 2004 .

[16]  T. Belytschko,et al.  Stability of an explicit multi-time step integration algorithm for linear structural dynamics equations , 1996 .

[17]  Charbel Farhat,et al.  Partitioned analysis of coupled mechanical systems , 2001 .

[18]  Ted Belytschko,et al.  Mixed-time implicit-explicit finite elements for transient analysis , 1982 .

[19]  D. Tortorelli,et al.  A FETI‐based domain decomposition technique for time‐dependent first‐order systems based on a DAE approach , 2008 .

[20]  Casadei Folco,et al.  Spatial Time Step Partitioning in Explicit Fast Transient Dynamics , 2008 .

[21]  Vincent Faucher,et al.  Local modal reduction in explicit dynamics with domain decomposition. Part 1: extension to subdomains undergoing finite rigid rotations , 2004 .

[22]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .