Partition of time unity for high frequency impacts on porous media
article
This paper presents a time integration scheme for relatively high frequency wave propagation in porous media. The scheme is based on the partition of unity method. The discontinuity is imposed on the velocity field, while the displacement field is kept continuous. The velocity discontinuity is postulated to occur in the time domain, alleviating thus the need for spatially tracing the wave front. Two formulations are derived. First, a general formulation, which describes the time discretization scheme on the basis of conventional and enhanced degrees of freedom, analogous to that of the standard partition of unity method. Second, a reduced formulation, which describes the time discretization scheme on the basis of conventional degrees of freedom only, analogous to the standard single-step time discretization algorithms, but keeping the notion of partition of unity, simply by letting the algorithmic parameter to move with time. The developed time integration scheme is unconditionally stable and has controllable numerical dissipation in the high frequency range. The time scheme has been implemented in combination with Biot's theory of wave propagation for modeling relatively high frequency stress waves in two-phase media. Numerical examples have been presented and demonstrated that the proposed time scheme is, in addition to being accurate and stable, highly effective for coarse meshes. This makes the developed scheme suitable for large scale finite element analysis.
Topics
TNO Identifier
881866
Source
International Journal for Numerical Methods in Engineering, pp. 1-22.
Pages
1-22
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