John David Moulton

A multilevel multiscale mimetic (M3) method for two-phase flows in porous media

We describe a multilevel multiscale mimetic (M^3) method for solving two-phase flow (water and oil) in a heterogeneous reservoir. The governing equations are the elliptic equation for the reservoir pressure and the hyperbolic equation for the water saturation. On each time step, we first solve the pressure equation and then use the computed flux in an explicit upwind finite volume method to update the saturation. To reduce the computational cost, the pressure equation is solved on a much coarser grid than the saturation equation. The coarse-grid pressure discretization captures the influence of multiple scales via the subgrid modeling technique for single-phase flow recently proposed in [Yu. A. Kuznetsov. Mixed finite element method for diffusion equations on polygonal meshes with mixed cells. J. Numer. Math., 14 (4) (2006) 305-315; V. Gvozdev. discretization of the diffusion and Maxwell equations on polyhedral meshes. Technical Report Ph.D. Thesis, University of Houston, 2007; Yu. Kuznetsov. Mixed finite element methods on polyhedral meshes for diffusion equations, in: Computational Modeling with PDEs in Science and Engineering, Springer-Verlag, Berlin, in press]. We extend significantly the applicability of this technique by developing a new robust and efficient method for estimating the flux coarsening parameters. Specifically, with this advance the M^3 method can handle full permeability tensors and general coarsening strategies, which may generate polygonal meshes on the coarse grid. These problem dependent coarsening parameters also play a critical role in the interpolation of the flux, and hence, in the advection of saturation for two-phase flow. Numerical experiments for two-phase flow in highly heterogeneous permeability fields, including layer 68 of the SPE Tenth Comparative Solution Project, demonstrate that the M^3 method retains good accuracy for high coarsening factors in both directions, up to 64 for the considered models. Moreover, we demonstrate that with a simple and efficient temporal updating strategy for the coarsening parameters, we achieve accuracy comparable to the fine-scale solution, but at a fraction of the cost.

Modeling challenges for predicting hydrologic response to degrading permafrost

The fate of the approximately 1,700 billion metric tons of carbon (Tarnocai et al. 2009) currently frozen in permafrost affected regions of the Arctic and subarctic is highly uncertain (IPCC 2007), primarily because of the potential for topographic evolution and resulting drainage network reorganization as permafrost degrades and massive ground ice contained in ice-rich permafrost soils melts. Computer modeling is a key tool in untangling these complex feedbacks to understand the evolution of the Arctic and subarctic landscapes and the potential feedbacks with the global climate system. Some of the challenges associated with modeling the hydrologic system in and around degrading permafrost are discussed in this essay. Modeling requirements depend very strongly on the spatial resolution of the model. Two different classes can be identified, depending on whether microtopography is explicitly resolved or incorporated into the model through a subgrid parameterization. The focus here is on the computational challenges associated with microtopography-resolving models using hydrologic response of polygon mires as an example. In such microtopography-resolving models, horizontal grid spacing on the order of 0.25mwould typically be required. Although highand low-centered ice wedge polygons have been identified as important controls on Arctic surface hydrology (e.g. Liljedahl et al. 2012) and evolution from lowto highcentered polygon landscapes is expected as Arctic temperatures increase (Jorgenson et al. 2006), as far as we are aware, there is no existing computer code that represents the full range of processes required to model the co-evolution of surface topography, active layer, and permafrost at the microtopography-resolving scale. For microtopography-resolving models of hydrology in permafrost landscapes, it is convenient to partition the large number of coupled processes into four critical sets: subsurface thermal/hydrology, surface thermal processes, mechanical deformation, and overland flow processes. However, it is important to recognize that the partitioning is somewhat arbitrary and that multiple tightly coupled processes exist within each set.

On the velocity space discretization for the Vlasov-Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

We describe a spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Markidis and Lapenta (2011) and Chen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier–Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC.

Future beam experiments in the magnetosphere with plasma contactors: How do we get the charge off the spacecraft?

The idea of using a high-voltage electron beam with substantial current to actively probe magnetic field line connectivity in space has been discussed since the 1970s. However, its experimental realization onboard a magnetospheric spacecraft has never been accomplished because the tenuous magnetospheric plasma cannot provide the return current necessary to keep spacecraft charging under control. In this work, we perform Particle-In-Cell simulations to investigate the conditions under which a high-voltage electron beam can be emitted from a spacecraft and explore solutions that can mitigate spacecraft charging. The electron beam cannot simply be compensated for by an ion beam of equal current, because the Child-Langmuir space charge limit is violated under conditions of interest. On the other hand, releasing a high-density neutral contactor plasma prior and during beam emission is critical in aiding beam emission. We show that after an initial transient controlled by the size of the contactor cloud where the spacecraft potential rises, the spacecraft potential can settle into conditions that allow for electron beam emission. A physical explanation of this result in terms of ion emission into spherical geometry from the surface of the plasma cloud is presented, together with scaling laws of the peak spacecraft potential varying the ion mass and beam current. These results suggest that a strategy where the contactor plasma and the electron beam operate simultaneously might offer a pathway to perform beam experiments in the magnetosphere.

Convolution-based particle tracking method for transient flow

A convolution-based particle tracking (CBPT) method was recently developed for calculating solute concentrations (Robinson et al., Comput Geosci 14(4): 779–792, 2010). This method is highly efficient but limited to steady-state flow conditions. Here, we present an extension of this method to transient flow conditions. This extension requires a single-particle tracking process model run, with a pulse of particles introduced at a sequence of times for each source location. The number and interval of particle releases depends upon the transients in the flow. Numerical convolution of particle paths obtained at each release time and location with a time-varying source term is performed to yield the shape of the plume. Many factors controlling transport such as variation in source terms, radioactive decay, and in some cases linear processes such as sorption and diffusion into dead-end pores can be simulated in the convolution step for Monte Carlo-based analysis of transport uncertainty. We demonstrate the efficiency of the transient CBPT method, by showing that it requires fewer particles than traditional random walk particle tracking methods to achieve the same levels of accuracy, especially as the source term increases in duration or is uncertain. Since flow calculations under transient conditions are often very expensive, this is a computationally efficient yet accurate method.

Future beam experiments in the magnetosphere with plasma contactors: The electron collection and ion emission routes

Experiments where a high-voltage electron beam emitted by a spacecraft in the low-density magnetosphere is used to probe the magnetospheric configuration could greatly enhance our understanding of the near-Earth environment. Their challenge, however, resides in the fact that the background magnetospheric plasma cannot provide a return current that balances the electron beam current without charging the spacecraft to such high potential that in practice prevents beam emission. In order to overcome this problem, a possible solution is based on the emission of a high-density contactor plasma by the spacecraft prior to and after the beam. We perform particle-in-cell simulations to investigate the conditions under which a high-voltage electron beam can be emitted from a magnetospheric spacecraft, comparing two possible routes that rely on the high-density contactor plasma. The first is an “electron collection” route, where the contactor has lower current than the electron beam and is used with the goal of connecting to the background plasma and collecting magnetospheric electrons over a much larger area than that allowed by the spacecraft alone. The second is an “ion emission” route, where the contactor has higher current than the electron beam. Ion emission is then enabled over the large quasi-spherical area of the contactor cloud, thus overcoming the space charge limits typical of ion beam emission. Our results indicate that the ion emission route offers a pathway for performing beam experiments in the low-density magnetosphere, while the electron collection route is not viable because the contactor fails to draw a large neutralizing current from the background.

Predicting Climate Feedbacks and Impacts in the Terrestrial Arctic: w14_terraarctic progress report

Regarding the Arctic Terrestrial Simulator (ATS), previous work solved integrated hydrology (coupled surface/subsurface flow) on multiple polygons, and surface flow over larger domains to guide landscape characterization. Solved thermal hydrology with freeze/thaw dynamics in three dimensions. Ongoing efforts apply state of the art thermal hydrology model to complex topography, and include mesh deformation processes.