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

Schmidt, Michael; Engdahl, Nicholas B.; Pankavich, Stephen; Bolster, Diogo

doi:10.1016/j.advwatres.2020.103577

Cited by 11 publications

(9 citation statements)

References 38 publications

(85 reference statements)

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“…is the normalized kernel that determines the weight of mass transfer between particles i and j [11], ρ ij is a normalizing constant that ensures conservation of mass and is typically taken to be the particle density [18,19], and s ij is the distance between particles i and j. We note that the choice of the Gaussian kernel's bandwidth is a free parameter.…”

Section: Model and Methodsmentioning

confidence: 99%

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

Thanh

Benson

Schmidt

et al. 2021

Advances in Water Resources

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Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the gain in accuracy of a highly discretized numerical model is outweighed by its associated computational costs or the noise within the data. We address the question of how many particles are needed in a simulation to best approximate and estimate parameters in one-dimensional advective-diffusive transport. To do so, we use the well-known Akaike Information Criterion (AIC) and a recently-developed correction called the Computational Information Criterion (COMIC) to guide the model selection process. Random-walk and mass-transfer particle tracking methods are employed to solve the model equations at various levels of discretization. Numerical results demonstrate that the COMIC provides an optimal number of particles that can describe a more efficient model in terms of parameter estimation and model prediction compared to the model selected by the AIC even when the data is sparse or noisy, the sampling volume is not uniform throughout the physical domain, or the error distribution of the data is non-IID Gaussian.

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Section: Model and Methodsmentioning

confidence: 99%

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

Thanh

Benson

Schmidt

et al. 2021

Advances in Water Resources

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show abstract

“…A substantial difference within this work is that the kernels are based on the local physics of diffusion, rather than a user-defined function chosen for attractive numerical qualities like compact support or controllable smoothness. This adherence to local physics allows for increased modeling fidelity, including the simulation of diffusion across material discontinuities or between immobile (solid) and mobile (fluid) species [30,19].…”

Section: Introductionmentioning

confidence: 99%

Parallelized Domain Decomposition for Multi-Dimensional Lagrangian Random Walk, Mass-Transfer Particle Tracking Schemes

Schauer¹,

Schmidt²,

Engdahl³

et al. 2022

Preprint

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We develop a multi-dimensional, parallelized domain decomposition strategy (DDC) for mass-transfer particle tracking (MTPT) methods. These methods are a type of Lagrangian algorithm for simulating reactive transport and are able to be parallelized by employing large numbers of CPU cores to accelerate run times. In this work, we investigate different procedures for "tiling" the domain in two and three dimensions, (2-d and 3-d), as this type of formal DDC construction is currently limited to 1-d. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-d for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-d parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run up to around 2700 cores, reducing a 5-hour simulation to 8 seconds, and the 3-d algorithm maintains appreciable speedup up to 1700 cores.

show abstract

Section: Introductionmentioning

confidence: 99%

Parallelized Domain Decomposition for Multi-Dimensional Lagrangian Random Walk, Mass-Transfer Particle Tracking Schemes

Schauer

Schmidt

Engdahl

et al. 2022

Preprint

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Abstract. Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for tiling the domain in two and three dimensions, (2-d and 3-d), as this type of formal DDC construction is currently limited to 1-d. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-d for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-d parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run up to around 2700 cores, reducing a 5-hour simulation to 8 seconds, while the 3-d algorithm maintains appreciable speedup up to 1700 cores.

show abstract

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

Cited by 11 publications

References 38 publications

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

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

Parallelized Domain Decomposition for Multi-Dimensional Lagrangian Random Walk, Mass-Transfer Particle Tracking Schemes

Parallelized Domain Decomposition for Multi-Dimensional Lagrangian Random Walk, Mass-Transfer Particle Tracking Schemes

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