Print Email Facebook Twitter A stable SPH discretization of the elliptic operator with heterogeneous coefficients Title A stable SPH discretization of the elliptic operator with heterogeneous coefficients Author Lukyanov, A. (TU Delft Numerical Analysis) Vuik, Cornelis (TU Delft Numerical Analysis) Date 2020 Abstract 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 of specific shape satisfying thetwo-point flux approximation nature 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 discretization methods are presented. Subject Diffusive flowDiscrete maximum principleLaplace operatorMeshless methodMonotone schemeStability and approximation To reference this document use: http://resolver.tudelft.nl/uuid:43a365b7-8b2e-42e4-91f6-2bcb0e16d2af DOI https://doi.org/10.1016/j.cam.2020.112745 ISSN 0377-0427 Source Journal of Computational and Applied Mathematics, 374 Part of collection Institutional Repository Document type journal article Rights © 2020 A. Lukyanov, Cornelis Vuik Files PDF 1_s2.0_S0377042720300364_main.pdf 4.84 MB Close viewer /islandora/object/uuid:43a365b7-8b2e-42e4-91f6-2bcb0e16d2af/datastream/OBJ/view