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DOE OSTI · 1803575

A mass-transfer particle-tracking method for simulating transport with discontinuous diffusion coefficients

Schmidt, Michael J.·Engdahl, Nicholas B.·Pankavich, Stephen D.·Bolster, Diogo
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Abstract

The problem of a spatially discontinuous diffusion coefficient (D(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(x). To achieve this, we derive a semi-analytical solution to the discontinuous D(x) problem by employing a predictor-corrector approach, and we use this semi-analytical solution as the weighting function in a reformulated MT algorithm. Furthermore, this semi-analytical solution is generalized for cases with multiple 1D interfaces as well as for 2D cases, including a 2 × 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.

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42 ENGINEERINGDiffusion-reaction equation' Composite porous mediaDiscontinuous diffusion coefficientsImperfect mixingLagrangian modelingMass-transfer particle-trackingParticle methodsWater resources

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Schmidt, Michael J., Engdahl, Nicholas B., Pankavich, Stephen D., Bolster, Diogo. 2020-03-25. A mass-transfer particle-tracking method for simulating transport with discontinuous diffusion coefficients. https://doi.org/10.1016/j.advwatres.2020.103577

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