A smoothed radial point interpolation method for application in porodynamics

Abstract

A meshfree numerical method for the dynamic analysis of porous media is presented. The u, p form of Biot's theory is adopted to mathematically model the dynamic interaction of the solid and the fluid phase within the porous media. The obtained partial differential equations (PDEs) are discretized by the generalized smoothed Galerkin weak form, which is established based on smoothed strains and fluxes. Therefore, edge-based and cell-based smoothing domains are used and a T3-scheme is employed for the selection of support nodes. The shape functions are generated by the radial point interpolation method. The focus of this work lies on the spatial integration of the mass/compressibility and coupling terms of the discrete PDE system. A new algorithm is introduced, which reuses the shape function values that are needed for the construction of the stiffness/permeability matrix to keep the computational effort at a minimum. Numerical problems are analyzed in order to test the algorithm regarding accuracy and efficiency.