Numerical simulation of comet nuclei I. Water-ice comets

A one-dimensional simulation of pure water-ice cometary nuclei is presented, and the effect of the nucleus as a heat reservoir is considered. The phase transition from amorphous to crystalline ice is studied for two cases: (1) where the released latent heat goes entirely into heating adjacent layers and (2) where the released latent heat goes entirely into sublimation. For a Halley-like orbit it was found that for case 1 the phase boundary penetrates about 15 m on the first orbit and does not advance until sublimation brings the surface to some 10 m from the phase boundary. For case 2 the phase boundary penetrates about 1 m below the surface and remains at this depth as the surface sublimates. For an orbit like that of Schwassmann-Wachmann 1 the phase boundary penetrates about 50 m initially for case 1 and about 1 m for case 2. There is no further transformation until the entire comet is heated slowly to near the transition temperature, after which the entire nucleus is converted to crystalline ice. For an Encke-type orbit case 1 gives a nearly continuous transition of the entire nucleus to crystalline ice, while for case 2 the initial penetration is about 8 m and remains at this depth relative to the surface as sublimation decreases the cometary radius. Thus the entire comet is converted to crystalline ice just before it is completely dissipated.     

Numerical simulations of comet nuclei: II. The effect of the dust mantle

The insulating effect of an evolving dust mantle is examined. The role of this mantle in determining the surface temperature of the ice core is studied as a function of the mass fraction of the dust in the ice-dust mixture and the thermal conductivity of the nucleus. Using the so-called “looselattice” model of D.A. Mendis and G.D. Brin (1977, Moon17, 359–372) (which was also extended to include cracks and pores in the mantle), it was found that both high dust to ice ratios and high core conductivities inhibit mantle blowoff. Indeed, it is often possible to build an essentially permanent dust mantle around an ice nucleus, so that the nucleus will take on an asteroidal appearance.     

Transient biouptake flux and accumulation by microorganisms: The case of two types of sites with Langmuir adsorption

The uptake of a chemical species by an aquatic microorganism is modelled considering two kinds of sites where Langmuirian adsorption is followed by first order internalisation kinetics. Simpler models, such as only one internalisation route (while most of the adsorption takes place on non-internalising sites) or a linear isotherm for adsorption on one or both sites, become limiting cases of this double-Langmuirian model. The model considers the sites located on the spherical (or semi-spherical) surface of the organism, and takes diffusion from the medium into explicit account. The numerical solution for the internalisation flux shows a maximum. We provide an estimate for the time needed to reach a certain proximity to steady state. The transient solution confirms that the analytical expressions for the steady-state flux are usually valid and that the accumulated amounts reflect the impact of the short-time uptake. The Instantaneous Steady-State Approximation (ISSA), where an intercept of the linear regression of accumulated amount as a function of time is interpreted as an adsorbed amount, can be critically assessed with the transient numerical code for two cases: (i) when the total burden of metal on the cell is the input data and (ii) when an extraction procedure provides further information on the adsorbed and internalised amount.     

Integration of local–global upscaling and grid adaptivity for simulation of subsurface flow in heterogeneous formations

We propose a methodology, called multilevel local–global (MLLG) upscaling, for generating accurate upscaled models of permeabilities or transmissibilities for flow simulation on adapted grids in heterogeneous subsurface formations. The method generates an initial adapted grid based on the given fine-scale reservoir heterogeneity and potential flow paths. It then applies local–global (LG) upscaling for permeability or transmissibility [7], along with adaptivity, in an iterative manner. In each iteration of MLLG, the grid can be adapted where needed to reduce flow solver and upscaling errors. The adaptivity is controlled with a flow-based indicator. The iterative process is continued until consistency between the global solve on the adapted grid and the local solves is obtained. While each application of LG upscaling is also an iterative process, this inner iteration generally takes only one or two iterations to converge. Furthermore, the number of outer iterations is bounded above, and hence, the computational costs of this approach are low. We design a new flow-based weighting of transmissibility values in LG upscaling that significantly improves the accuracy of LG and MLLG over traditional local transmissibility calculations. For highly heterogeneous (e.g., channelized) systems, the integration of grid adaptivity and LG upscaling is shown to consistently provide more accurate coarse-scale models for global flow, relative to reference fine-scale results, than do existing upscaling techniques applied to uniform grids of similar densities. Another attractive property of the integration of upscaling and adaptivity is that process dependency is strongly reduced, that is, the approach computes accurate global flow results also for flows driven by boundary conditions different from the generic boundary conditions used to compute the upscaled parameters. The method is demonstrated on Cartesian cell-based anisotropic refinement (CCAR) grids, but it can be applied to other adaptation strategies for structured grids and extended to unstructured grids.     

Accurate local upscaling with variable compact multipoint transmissibility calculations

We propose a new single-phase local upscaling method that uses spatially varying multipoint transmissibility calculations. The method is demonstrated on two-dimensional Cartesian and adaptive Cartesian grids. For each cell face in the coarse upscaled grid, we create a local fine grid region surrounding the face on which we solve two generic local flow problems. The multipoint stencils used to calculate the fluxes across coarse grid cell faces involve the six neighboring pressure values. They are required to honor the two generic flow problems. The remaining degrees of freedom are used to maximize compactness and to ensure that the flux approximation is as close as possible to being two-point. The resulting multipoint flux approximations are spatially varying (a subset of the six neighbors is adaptively chosen) and reduce to two-point expressions in cases without full-tensor anisotropy. Numerical tests show that the method significantly improves upscaling accuracy as compared to commonly used local methods and also compares favorably with a local–global upscaling method.