Efficient modelling of solute transport in heterogeneous media with discrete event simulation

Abstract

To address the problem of different time scales present in the simulation of solute transport through systems with a complex permeability structure such as fractured porous rocks, we propose a parallel discrete event simulation (DES) algorithm based on local time stepping criteria, specifically developed for the hybrid finite-element node-centred finite volume (FV) framework. A preemptive-event-processing (PEP) approach is applied to synchronise discrete events with sufficiently close time stamps, thereby facilitating the parallelisation for shared memory architectures. The accuracy of the presented DES-PEP scheme is first verified against the analytical solution of a 1D advection equation with spatially variable coefficients. The DES scheme is then applied to simulate tracer advection through a 3D model of highly heterogeneous fractured rock represented by an unstructured adaptively refined mesh with over 1 million elements. DES produces results comparable to those of a conventional time-driven simulation (TDS), but uses less than 1% of the execution time. Analysis of event distributions shows that updates occur almost exclusively in a small number of FV cells marked by order-of-magnitudes faster fluid flow and advection-dominated transfer, while slow-flowing cells remain inactive and excluded from computations. This focusing of the computational effort leads to high simulation efficiency while simultaneously diminishing round-off errors. Scalability tests with a parallel version of DES on shared memory demonstrate further computational speedups mirroring the increased number of threads. With the use of 20 threads, execution time is reduced from 42.5 days (with TDS) to only 1.5 hours, equivalent to a speedup of over 670. This parallel DES algorithm therefore enables efficient multi-core simulation of solute transport in heterogeneous geologically realistic systems.