Speaker
Description
Describing the transport of scalars such as nutrients and contaminants in heterogeneous systems presents both computational and modeling challenges and can lead to a rich set of behaviors across different scales. Random walk particle tracking methods offer an alternative to more traditional Eulerian approaches that involves discretizing the transported plume into point masses. Each resulting point particle moves along a trajectory governed by a stochastic (Langevin) differential equation. The concentration field of the transported scalar is then identified with the probability density of particle positions.
Particle tracking methods for transport are fundamentally free from the instabilities that Eulerian methods are prone to in advection-dominated systems. In addition, because they do not implicitly homogenize concentrations over an underlying grid, they mitigate numerical dispersion. From a computational standpoint, since particles represent possible physical trajectories, computational power is naturally localized where mass is present, and locally-adaptive time steps can be employed. For these reasons, particle tracking methods excel at resolving plume structures for scalar concentration fields that are relatively localized in space but exhibit complex structure. This makes them particularly interesting to model processes that are highly sensitive to local concentration fluctuations, such as mixing and reaction.
Despite their potential advantages, the application of random walk particle tracking methods to heterogeneous media has been mainly restricted to time-independent conditions and, correspondingly, static boundary conditions. In the presence of multiple fluids, if a chemical species is restricted to a specific phase or otherwise interacts with fluid-fluid interfaces, significant challenges arise unless the phase configuration is frozen. In this talk, we present an extension of particle tracking methods to fully time-dependent, two-phase flow conditions, where the restriction of a transported species to one of the fluid phases is handled through the application of a chemical potential that takes a lower value in the carrier phase. Particles feel an effective drift near the fluid-fluid interface that is proportional to the potential difference between the two phases, leading to a concentration ratio that follows Henry's law. By increasing this potential difference, the amount of mass that crosses the interface can be made arbitrarily small. This formulation only requires knowledge of the flow and saturation fields, avoiding explicit reconstruction of phase boundaries and direct computation of particle reflection at fluid-fluid interfaces. We illustrate the application of the method to the simulation of mixing fronts in heterogeneous media under two-phase flow conditions, and we discuss possible extensions to more complex interface phenomena.
| Country | Spain |
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