Smooth Particle Hydrodynamics with nonlinear Moving-Least-Squares WENO reconstruction to model anisotropic dispersion in porous media |
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| Affiliation: | 1. Department of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano 77, I-38123 Trento, Italy;2. Department of Civil Engineering, University of Chile, Av. Blanco Encalada 2002, Santiago 8370449, Chile;3. Center for Applied Geoscience, University of Tübingen, Hölderlinstr. 12, 72074 Tübingen, Germany;4. Faculty for Civil, Geo and Environmental Engineering, Technical University of Munich, Darcistrasse 21, 80333 Munich, Germany;1. College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China;2. Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA;1. Department of Earth and Environment, Boston University, Boston 02215, United States;2. Louisiana Universities Marine Consortium, Chauvin, LA 70344, United States;1. Institute for Computational Engineering and Sciences, 201 E. 24th St., Stop C0200, University of Texas at Austin, Austin, TX 78712, United States;2. Coastal and Hydraulics Laboratory, U.S. Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180-6199, United States;1. Chaire de recherche EDS en prévisions et actions hydrologiques, Université Laval, Québec, Canada;2. Department of Civil and Water Engineering, pavillon Adrien-Pouliot, 1065, avenue de la Médecine, Université Laval, Québec, Canada;3. Recherche en prévision numérique environnementale, Environnement Canada, 2121, route Transcanadienne Dorval, Montréal, Québec H9P 1J3, Canada |
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| Abstract: | Most numerical schemes applied to solve the advection–diffusion equation are affected by numerical diffusion. Moreover, unphysical results, such as oscillations and negative concentrations, may emerge when an anisotropic dispersion tensor is used, which induces even more severe errors in the solution of multispecies reactive transport. To cope with this long standing problem we propose a modified version of the standard Smoothed Particle Hydrodynamics (SPH) method based on a Moving-Least-Squares-Weighted-Essentially-Non-Oscillatory (MLS-WENO) reconstruction of concentrations. This scheme formulation (called MWSPH) approximates the diffusive fluxes with a Rusanov-type Riemann solver based on high order WENO scheme. We compare the standard SPH with the MWSPH for different a few test cases, considering both homogeneous and heterogeneous flow fields and different anisotropic ratios of the dispersion tensor. We show that, MWSPH is stable and accurate and that it reduces the occurrence of negative concentrations compared to standard SPH. When negative concentrations are observed, their absolute values are several orders of magnitude smaller compared to standard SPH. In addition, MWSPH limits spurious oscillations in the numerical solution more effectively than classical SPH. Convergence analysis shows that MWSPH is computationally more demanding than SPH, but with the payoff a more accurate solution, which in addition is less sensitive to particles position. The latter property simplifies the time consuming and often user dependent procedure to define the initial dislocation of the particles. |
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| Keywords: | Smooth Particle Hydrodynamics (SPH) Moving-Least-Squares (MLS) WENO reconstruction Meshless Lagrangian particle methods Anisotropic dispersion Porous media |
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