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A Stable SPH Discretization of the Elliptic Operator with Heterogeneous Coefficients. (arXiv:1711.11351v1 [math.NA])
来源于:arXiv
Smoothed particle hydrodynamics (SPH) has been extensively used to model high
and low Reynolds number flows, free surface flows and collapse of dams, study
pore-scale flow and dispersion, elasticity, and thermal problems. In different
applications, it is required to have a stable and accurate discretization of
the elliptic operator with homogeneous and heterogeneous coefficients. In this
paper, the stability and approximation analysis of different SPH discretization
schemes (traditional and new) of the diagonal elliptic operator for homogeneous
and heterogeneous media are presented. The optimum and new discretization
scheme is also proposed. This scheme enhances the Laplace approximation
(Brookshaw's scheme (1985) and Schwaiger's scheme (2008)) used in the SPH
community for thermal, viscous, and pressure projection problems with an
isotropic elliptic operator. The numerical results are illustrated by numerical
examples, where the comparison between different versions of the meshless
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