A Mass-transfer Particle-tracking Method for Simulating Transport with Discontinuous Diffusion Coefficients

Abstract

The problem of a spatially discontinuous diffusion coefficient ($D(\mathbf{x})$) is one that may be encountered in hydrogeologic systems due to natural geological features or as a consequence of numerical discretization of flow properties. To date, mass-transfer particle-tracking (MTPT) methods, a family of Lagrangian methods in which diffusion is jointly simulated by random walk and diffusive mass transfers, have been unable to solve this problem. This manuscript presents a new mass-transfer (MT) algorithm that enables MTPT methods to accurately solve the problem of discontinuous $D(\mathbf{x})$. To achieve this, we derive a semi-analytical solution to the discontinuous $D(\mathbf{x})$ problem by employing a predictor-corrector approach, and we use this semi-analytical solution as the weighting function in a reformulated MT algorithm. This semi-analytical solution is generalized for cases with multiple 1D interfaces as well as for 2D cases, including a $2\times 2$ tiling of 4 subdomains that corresponds to a numerically-generated diffusion field. The solutions generated by this new mass-transfer algorithm closely agree with an analytical 1D solution or, in more complicated cases, trusted numerical results, demonstrating the success of our proposed approach.

26 pages, 11 figures

References in corpus (7)

• On the separate treatment of mixing and spreading by the reactive-particle-tracking algorithm: An example of accurate upscaling of reactive Poiseuille flow
• A Kernel-based Lagrangian Method for Imperfectly-mixed Chemical Reactions
• Accelerating and parallelizing Lagrangian simulations of mixing-limited reactive transport
• Particle Density Estimation with Grid-Projected Adaptive Kernels
• On the accuracy of simulating mixing by random-walk particle-based mass-transfer algorithms
• Numerical Equivalence Between SPH and Probabilistic Mass Transfer Methods for Lagrangian Simulation of Dispersion
• Reactive Particle-tracking Solutions to a Benchmark Problem on Heavy Metal Cycling in Lake Sediments

Cited by in corpus (1)

• A Computational Information Criterion for Particle-Tracking with Sparse or Noisy Data