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Diagonally Staggered Grid for Elastodynamic Analysis Using the Finite-Difference Time-Domain Method

A new diagonally staggered grid configuration is proposed for the finite-difference time-domain analysis of elastic wave fields. The structure of the grid is the same as a standard staggered grid, but the diagonals of the standard grid lie parallel to the coordinate axes of the field of analysis in this new configuration. Adopting this grid configuration allows a natural implementation of antisymmetric stress boundary conditions, as is required when implementing free boundaries for example. In implementing these boundary conditions no virtual lattice around the analysis region is required, and so free surfaces with complex boundary shapes are easily treated. To date, free boundaries have usually been treated using the zero-stress formulation (ZSF), the vacuum formulation (VCF), etc. The ZSF is relatively precise, but requires the creation of virtual grids in the vacuum region. On the other hand, the VCF does not require the use of virtual grids, but accuracy and stability are reduced relative to the ZSF. Also, other methods of free boundary implementation have some demerits. The validity of the diagonally staggered grid is confirmed by comparing the calculation results of the present scheme with those derived by existing finite-difference methods for a model test problem.