GPU accelerated parallel contaminant transport due to physical heterogeneity and mobile immobile mass transfer by integrating meshless radial point collocation method and variants of random walk

Abstract

We propose two coupled models for subsurface flow and contaminant transport simulation by combining the mesh-free radial point collocation method (RPCM) separately with random walk particle tracking (RWPT) and continuous-time random walk particle tracking (CTRWPT). The RPCM is suitable for adaptive remeshing and modeling aquifers with complicated aquifer geometries due to the use of scattered nodes. This study considers a highly heterogeneous unconfined aquifer whose hydraulic head and seepage velocity distributions are generated using RPCM. Hydraulic head distribution obtained using RPCM closely resemble the solution of the finite difference method (FDM). The velocity distribution is used further by RWPT to simulate the advection-dispersion equation (ADE) for impulse and continuous contaminant injections. The RWPT is also free from numerical dispersion and thus more accurate for solving ADE than the Eulerian transport models. However, similar to Eulerian transport models, the RWPT cannot accurately approximate the dispersive nature of mobile-immobile mass transfer (MIMT) as it approximates retarded ADE (RADE) under the assumptions of local equilibrium. Hence, this study proposes a novel algorithm, namely CTRWPT, that modifies RWPT to approximate MIMT. The CTRWPT model is applied successfully to simulate transport processes with assumed MIMT parameters in the heterogeneous unconfined aquifer. We further proved that the CTRWPT converges with RADE when the effective late time Fickian dispersion coefficient is sufficiently small. In this study, the contaminant transport simulation involving RWPT and CTRWPT is carried out in the graphical processing unit (GPU) using CUDA (Compute Unified Device Architecture) with 3 million particles. The GPU implementation of the RWPT and CTRWPT models achieves computational speedups of 110 folds and 40 folds, respectively, compared to the analogous CPU implementation.