Simulation of the transport of particles in coastal waters using forward and reverse time diffusion

Spivakovskaya, D.; Heemink, A.W.; Milstein, Grigori N.; Schoenmakers, John

doi:10.1016/j.advwatres.2005.03.005

Cited by 20 publications

(13 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Two alternative differential equations have been developed [see, e.g., Gardiner , 1983]: the forward Fokker‐Planck equation (FPE) and the backward‐in‐time Kolmogorov equation (BKE) [ Kolmogorov , 1931]. The use of forward and backward models for location and travel time probability has become a classical mathematical approach for contaminant transport characterization and prediction [ Uffink , 1989; LaBolle et al , 1998; Varni and Carrera , 1998; Neupauer and Wilson , 1999; Spivakovskaya et al , 2005]. The forward version of the Fokker‐Planck equations points to the future, and the transformation from probabilities and particle densities to a physical concept of a solute concentration is straightforward.…”

Section: Theorymentioning

confidence: 99%

Use of groundwater lifetime expectancy for the performance assessment of a deep geologic waste repository: 1. Theory, illustrations, and implications

Cornaton

Park

Normani

et al. 2008

Water Resources Research

View full text Add to dashboard Cite

[1] Long-term solutions for the disposal of toxic wastes usually involve isolation of the wastes in a deep subsurface geologic environment. In the case of spent nuclear fuel, if radionuclide leakage occurs from the engineered barrier, the geological medium represents the ultimate barrier that is relied upon to ensure safety. Consequently, an evaluation of radionuclide travel times from a repository to the biosphere is critically important in a performance assessment analysis. In this study, we develop a travel time framework based on the concept of groundwater lifetime expectancy as a safety indicator. Lifetime expectancy characterizes the time that radionuclides will spend in the subsurface after their release from the repository and prior to discharging into the biosphere. The probability density function of lifetime expectancy is computed throughout the host rock by solving the backward-in-time solute transport adjoint equation subject to a properly posed set of boundary conditions. It can then be used to define optimal repository locations. The risk associated with selected sites can be evaluated by simulating an appropriate contaminant release history. The utility of the method is illustrated by means of analytical and numerical examples, which focus on the effect of fracture networks on the uncertainty of evaluated lifetime expectancy.

show abstract

Section: Theorymentioning

confidence: 99%

Use of groundwater lifetime expectancy for the performance assessment of a deep geologic waste repository: 1. Theory, illustrations, and implications

Cornaton

Park

Normani

et al. 2008

Water Resources Research

View full text Add to dashboard Cite

show abstract

“…These particle models can deal easily with arbitrarily steep concentration gradients and are strictly mass conserving. More recently variance reduction methods have been applied in order to increase the efficiency of the particle models [16,17].…”

Section: Introductionmentioning

confidence: 99%

Identification of ground water flow patterns using particle models

Serafy

Heemink

Geer³

2008

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

Particle models are often used to simulate transport processes in ground water. The ground water flow pattern is one of the driving parameters of the transport model. In this paper a parameter identification algorithm is developed for particle type models to identify the underlying flow pattern from concentration measurements. The estimation problem is solved with a gradient based algorithm. For each generated particle track, the adjoint track is determined to efficiently compute gradient of the criterion.

show abstract

“…Choosing a Lagrangian approach [59], [60], we solve the advective and diffusive dynamics of point particles that represent the solid phase, but are not the same as the particles of the suspension itself. The dynamics of such particles is then described as random walks based on stochastic differential equations which are consistent with the advection-diffusion equation.…”

Section: 3mentioning

confidence: 99%