GPU implementation of Eulerian methods with TVD schemes for solving 2D solute transport in heterogeneous flows

Abstract:

In this work we present an efficient implementation of Eulerian TVD methods in uniform Cartesian meshes. We apply parallelization strategies based entirely on GPU for the solution of the 2D transport and flow equation in heterogeneous porous media. Additionally, a parallel strategy is proposed for the generation of exponentially correlated lognormally distributed permeability fields in GPU. The programs are developed using the C ++ / CUDA language. The implemented methods are used to solve advective dominant problems, in a context of Monte Carlo (MC) type simulations to numerically determine the longitudinal and transversal macrodispersion coefficients averaging over 100 simulations for permeability fields in a range of variances between 0.25, 1, 2.25, 4 and 6.25. The following types of transport are considered for testing: pure advection, advection-diffusion and advection-dispersion. The performance in terms of the computation time of explicit and implicit methods are compared. We show that the implemented algorithms allow to efficiently solve problems in computational domains of up to 134.5 million cells using an Eulerian method on modern GPU processors.