Multiscale descriptions of density-driven flow instabilities in porous media

Les instabilités engendrées par des gradients de densité interviennent dans une variété d'écoulements. Un exemple est celui de la séquestration géologique du dioxyde de carbone en milieux poreux. Ce gaz est injecté à haute pression dans des aquifères salines et profondes. La différence de densité entre la saumure saturée en CO2 dissous et la saumure environnante induit des courants favorables qui le transportent vers les couches géologiques profondes. Les gradients de densité peuvent aussi être la cause du transport indésirable de matières toxiques, ce qui peut éventuellement conduire à la pollution des sols et des eaux. La gamme d'échelles intervenant dans ce type de phénomènes est très large. Elle s'étend de l'échelle poreuse où les phénomènes de croissance des instabilités s'opèrent, jusqu'à l'échelle des aquifères à laquelle interviennent les phénomènes à temps long. Une reproduction fiable de la physique par la simulation numérique demeure donc un défi en raison du caractère multi-échelles aussi bien au niveau spatial et temporel de ces phénomènes. Il requiert donc le développement d'algorithmes performants et l'utilisation d'outils de calculs modernes. En conjugaison avec les méthodes de résolution itératives, les méthodes multi-échelles permettent de résoudre les grands systèmes d'équations algébriques de manière efficace. Ces méthodes ont été introduites comme méthodes d'upscaling et de downscaling pour la simulation d'écoulements en milieux poreux afin de traiter de fortes hétérogénéités du champ de perméabilité. Le principe repose sur l'utilisation parallèle de deux maillages, le premier est choisi en fonction de la résolution du champ de perméabilité (grille fine), alors que le second (grille grossière) est utilisé pour approximer le problème fin à moindre coût. La qualité de la solution multi-échelles peut être améliorée de manière itérative pour empêcher des erreurs trop importantes si le champ de perméabilité est complexe. Les méthodes adaptatives qui restreignent les procédures de mise à jour aux régions à forts gradients permettent de limiter les coûts de calculs additionnels. Dans le cas d'instabilités induites par des gradients de densité, l'échelle des phénomènes varie au cours du temps. En conséquence, des méthodes multi-échelles adaptatives sont requises pour tenir compte de cette dynamique. L'objectif de cette thèse est de développer des algorithmes multi-échelles adaptatifs et efficaces pour la simulation des instabilités induites par des gradients de densité. Pour cela, nous nous basons sur la méthode des volumes finis multi-échelles (MsFV) qui offre l'avantage de résoudre les phénomènes de transport tout en conservant la masse de manière exacte. Dans la première partie, nous pouvons démontrer que les approximations de la méthode MsFV engendrent des phénomènes de digitation non-physiques dont la suppression requiert des opérations de correction itératives. Les coûts de calculs additionnels de ces opérations peuvent toutefois être compensés par des méthodes adaptatives. Nous proposons aussi l'utilisation de la méthode MsFV comme méthode de downscaling: la grille grossière étant utilisée dans les zones où l'écoulement est relativement homogène alors que la grille plus fine est utilisée pour résoudre les forts gradients. Dans la seconde partie, la méthode multi-échelle est étendue à un nombre arbitraire de niveaux. Nous prouvons que la méthode généralisée est performante pour la résolution de grands systèmes d'équations algébriques. Dans la dernière partie, nous focalisons notre étude sur les échelles qui déterminent l'évolution des instabilités engendrées par des gradients de densité. L'identification de la structure locale ainsi que globale de l'écoulement permet de procéder à un upscaling des instabilités à temps long alors que les structures à petite échelle sont conservées lors du déclenchement de l'instabilité. Les résultats présentés dans ce travail permettent d'étendre les connaissances des méthodes MsFV et offrent des formulations multi-échelles efficaces pour la simulation des instabilités engendrées par des gradients de densité. - Density-driven instabilities in porous media are of interest for a wide range of applications, for instance, for geological sequestration of CO2, during which CO2 is injected at high pressure into deep saline aquifers. Due to the density difference between the C02-saturated brine and the surrounding brine, a downward migration of CO2 into deeper regions, where the risk of leakage is reduced, takes place. Similarly, undesired spontaneous mobilization of potentially hazardous substances that might endanger groundwater quality can be triggered by density differences. Over the last years, these effects have been investigated with the help of numerical groundwater models. Major challenges in simulating density-driven instabilities arise from the different scales of interest involved, i.e., the scale at which instabilities are triggered and the aquifer scale over which long-term processes take place. An accurate numerical reproduction is possible, only if the finest scale is captured. For large aquifers, this leads to problems with a large number of unknowns. Advanced numerical methods are required to efficiently solve these problems with today's available computational resources. Beside efficient iterative solvers, multiscale methods are available to solve large numerical systems. Originally, multiscale methods have been developed as upscaling-downscaling techniques to resolve strong permeability contrasts. In this case, two static grids are used: one is chosen with respect to the resolution of the permeability field (fine grid); the other (coarse grid) is used to approximate the fine-scale problem at low computational costs. The quality of the multiscale solution can be iteratively improved to avoid large errors in case of complex permeability structures. Adaptive formulations, which restrict the iterative update to domains with large gradients, enable limiting the additional computational costs of the iterations. In case of density-driven instabilities, additional spatial scales appear which change with time. Flexible adaptive methods are required to account for these emerging dynamic scales. The objective of this work is to develop an adaptive multiscale formulation for the efficient and accurate simulation of density-driven instabilities. We consider the Multiscale Finite-Volume (MsFV) method, which is well suited for simulations including the solution of transport problems as it guarantees a conservative velocity field. In the first part of this thesis, we investigate the applicability of the standard MsFV method to density- driven flow problems. We demonstrate that approximations in MsFV may trigger unphysical fingers and iterative corrections are necessary. Adaptive formulations (e.g., limiting a refined solution to domains with large concentration gradients where fingers form) can be used to balance the extra costs. We also propose to use the MsFV method as downscaling technique: the coarse discretization is used in areas without significant change in the flow field whereas the problem is refined in the zones of interest. This enables accounting for the dynamic change in scales of density-driven instabilities. In the second part of the thesis the MsFV algorithm, which originally employs one coarse level, is extended to an arbitrary number of coarse levels. We prove that this keeps the MsFV method efficient for problems with a large number of unknowns. In the last part of this thesis, we focus on the scales that control the evolution of density fingers. The identification of local and global flow patterns allows a coarse description at late times while conserving fine-scale details during onset stage. Results presented in this work advance the understanding of the Multiscale Finite-Volume method and offer efficient dynamic multiscale formulations to simulate density-driven instabilities. - Les nappes phréatiques caractérisées par des structures poreuses et des fractures très perméables représentent un intérêt particulier pour les hydrogéologues et ingénieurs environnementaux. Dans ces milieux, une large variété d'écoulements peut être observée. Les plus communs sont le transport de contaminants par les eaux souterraines, le transport réactif ou l'écoulement simultané de plusieurs phases non miscibles, comme le pétrole et l'eau. L'échelle qui caractérise ces écoulements est définie par l'interaction de l'hétérogénéité géologique et des processus physiques. Un fluide au repos dans l'espace interstitiel d'un milieu poreux peut être déstabilisé par des gradients de densité. Ils peuvent être induits par des changements locaux de température ou par dissolution d'un composé chimique. Les instabilités engendrées par des gradients de densité revêtent un intérêt particulier puisque qu'elles peuvent éventuellement compromettre la qualité des eaux. Un exemple frappant est la salinisation de l'eau douce dans les nappes phréatiques par pénétration d'eau salée plus dense dans les régions profondes. Dans le cas des écoulements gouvernés par les gradients de densité, les échelles caractéristiques de l'écoulement s'étendent de l'échelle poreuse où les phénomènes de croissance des instabilités s'opèrent, jusqu'à l'échelle des aquifères sur laquelle interviennent les phénomènes à temps long. Etant donné que les investigations in-situ sont pratiquement impossibles, les modèles numériques sont utilisés pour prédire et évaluer les risques liés aux instabilités engendrées par les gradients de densité. Une description correcte de ces phénomènes repose sur la description de toutes les échelles de l'écoulement dont la gamme peut s'étendre sur huit à dix ordres de grandeur dans le cas de grands aquifères. Il en résulte des problèmes numériques de grande taille qui sont très couteux à résoudre. Des schémas numériques sophistiqués sont donc nécessaires pour effectuer des simulations précises d'instabilités hydro-dynamiques à grande échelle. Dans ce travail, nous présentons différentes méthodes numériques qui permettent de simuler efficacement et avec précision les instabilités dues aux gradients de densité. Ces nouvelles méthodes sont basées sur les volumes finis multi-échelles. L'idée est de projeter le problème original à une échelle plus grande où il est moins coûteux à résoudre puis de relever la solution grossière vers l'échelle de départ. Cette technique est particulièrement adaptée pour résoudre des problèmes où une large gamme d'échelle intervient et évolue de manière spatio-temporelle. Ceci permet de réduire les coûts de calculs en limitant la description détaillée du problème aux régions qui contiennent un front de concentration mobile. Les aboutissements sont illustrés par la simulation de phénomènes tels que l'intrusion d'eau salée ou la séquestration de dioxyde de carbone.

Ambient vertical flow in long-screen wells: a case study in the Fontainebleau Sands Aquifer (France)

A tritium (H-3) profile was constructed in a long-screened well (LSW) of the Fontainebleau Sands Aquifer (France), and the data were combined with temperature logs to gain insight into the potential effects of the ambient vertical flow (AVF) of water through the well on the natural aquifer stratification. AVF is commonly taken into account in wells located in fracture aquifers or intercepting two different aquifers with distinct hydraulic heads. However, due to the vertical hydraulic gradient of the flow lines intercepted by wells, AVF of groundwater is a common process within any type of aquifer. The detection of 3H in the deeper parts of the studied well ( approximate depth 50m), where H-3-free groundwater is expected, indicates that shallow young water is being transported downwards through the well itself. The temperature logs show a nearly zero gradient with depth, far below the mean geothermal gradient in sedimentary basins. The results show that the age distribution of groundwater samples might be biased in relation to the age distribution in the surroundings of the well. The use of environmental tracers to investigate aquifer properties, particularly in LSWs, is then limited by the effects of the AVF of water that naturally occurs through the well.

Hybrid Multiscale Finite Volume method for two-phase flow in porous media

We present a novel hybrid (or multiphysics) algorithm, which couples pore-scale and Darcy descriptions of two-phase flow in porous media. The flow at the pore-scale is described by the Navier?Stokes equations, and the Volume of Fluid (VOF) method is used to model the evolution of the fluid?fluid interface. An extension of the Multiscale Finite Volume (MsFV) method is employed to construct the Darcy-scale problem. First, a set of local interpolators for pressure and velocity is constructed by solving the Navier?Stokes equations; then, a coarse mass-conservation problem is constructed by averaging the pore-scale velocity over the cells of a coarse grid, which act as control volumes; finally, a conservative pore-scale velocity field is reconstructed and used to advect the fluid?fluid interface. The method relies on the localization assumptions used to compute the interpolators (which are quite straightforward extensions of the standard MsFV) and on the postulate that the coarse-scale fluxes are proportional to the coarse-pressure differences. By numerical simulations of two-phase problems, we demonstrate that these assumptions provide hybrid solutions that are in good agreement with reference pore-scale solutions and are able to model the transition from stable to unstable flow regimes. Our hybrid method can naturally take advantage of several adaptive strategies and allows considering pore-scale fluxes only in some regions, while Darcy fluxes are used in the rest of the domain. Moreover, since the method relies on the assumption that the relationship between coarse-scale fluxes and pressure differences is local, it can be used as a numerical tool to investigate the limits of validity of Darcy's law and to understand the link between pore-scale quantities and their corresponding Darcy-scale variables.

Error estimate and control in the MSFV method for multiphase flow in porous media

n this paper the iterative MSFV method is extended to include the sequential implicit simulation of time dependent problems involving the solution of a system of pressure-saturation equations. To control numerical errors in simulation results, an error estimate, based on the residual of the MSFV approximate pressure field, is introduced. In the initial time steps in simulation iterations are employed until a specified accuracy in pressure is achieved. This initial solution is then used to improve the localization assumption at later time steps. Additional iterations in pressure solution are employed only when the pressure residual becomes larger than a specified threshold value. Efficiency of the strategy and the error control criteria are numerically investigated. This paper also shows that it is possible to derive an a-priori estimate and control based on the allowed pressure-equation residual to guarantee the desired accuracy in saturation calculation.

Genetic clusters and sex-biased gene flow in a unicolonial Formica ant.

BACKGROUND: Animal societies are diverse, ranging from small family-based groups to extraordinarily large social networks in which many unrelated individuals interact. At the extreme of this continuum, some ant species form unicolonial populations in which workers and queens can move among multiple interconnected nests without eliciting aggression. Although unicoloniality has been mostly studied in invasive ants, it also occurs in some native non-invasive species. Unicoloniality is commonly associated with very high queen number, which may result in levels of relatedness among nestmates being so low as to raise the question of the maintenance of altruism by kin selection in such systems. However, the actual relatedness among cooperating individuals critically depends on effective dispersal and the ensuing pattern of genetic structuring. In order to better understand the evolution of unicoloniality in native non-invasive ants, we investigated the fine-scale population genetic structure and gene flow in three unicolonial populations of the wood ant F. paralugubris. RESULTS: The analysis of geo-referenced microsatellite genotypes and mitochondrial haplotypes revealed the presence of cryptic clusters of genetically-differentiated nests in the three populations of F. paralugubris. Because of this spatial genetic heterogeneity, members of the same clusters were moderately but significantly related. The comparison of nuclear (microsatellite) and mitochondrial differentiation indicated that effective gene flow was male-biased in all populations. CONCLUSION: The three unicolonial populations exhibited male-biased and mostly local gene flow. The high number of queens per nest, exchanges among neighbouring nests and restricted long-distance gene flow resulted in large clusters of genetically similar nests. The positive relatedness among clustermates suggests that kin selection may still contribute to the maintenance of altruism in unicolonial populations if competition occurs among clusters.

Nestling detectability affects parental feeding preferences in a cavity-nesting bird

In many avian species, nestlings have evolved striking plumage, behaviours and mouth colours to obtain a greater share of parental investment. Studies revealing parental feeding preferences for nestlings with red gapes have proposed that red mouth colour in songbirds can act as a signal of nestling need or condition. Alternative hypotheses suggest that bright nestling mouths in cavity-nesting birds evolved to increase nestling detectability by the parents. We tested whether nestling mouth colour affects parental feeding preferences in great tits, Pants major L. In broods of six young, we experimentally painted mouth gapes and flanges either red or yellow and tested the effect of mouth colour on nestlings' mass gain under two lighting conditions. In nests with high luminosity, there was no significant effect of mouth colour on mass gain. In nests with low luminosity, nestlings with red gapes and flanges gained less mass than nestlings with red gapes and yellow flanges or both yellow gapes and flanges. Our results suggest that, in nests with low luminosity, red mouths decreased nestling detectability to the feeding parents and support the hypothesis that poor luminosity in nesting cavities can select for pale mouths. Overall, our results do not support the hypothesis that red mouth colour signals nestling need or condition to parent great tits.

Chromosomal rearrangements do not seem to affect the gene flow in hybrid zones between karyotypic races of the common shrew (Sorex araneus).

Chromosomal rearrangements are proposed to promote genetic differentiation between chromosomally differentiated taxa and therefore promote speciation. Due to their remarkable karyotypic polymorphism, the shrews of the Sorex araneus group were used to investigate the impact of chromosomal rearrangements on gene flow. Five intraspecific chromosomal hybrid zones characterized by different levels of karyotypic complexity were studied using 16 microsatellites markers. We observed low levels of genetic differentiation even in the hybrid zones with the highest karyotypic complexity. No evidence of restricted gene flow between differently rearranged chromosomes was observed. Contrary to what was observed at the interspecific level, the effect of chromosomal rearrangements on gene flow was undetectable within the S. araneus species.

Vasopressin-dependent coupling between sodium transport and water flow in a mouse cortical collecting duct cell line.

Water balance is achieved through the ability of the kidney to control water reabsorption in the connecting tubule and the collecting duct. In a mouse cortical collecting duct cell line (mCCD(c11)), physiological concentrations of arginine vasopressin increased both electrogenic, amiloride-sensitive, epithelial sodium channel (ENaC)-mediated sodium transport measured by the short-circuit current (Isc) method and water flow (Jv apical to basal) measured by gravimetry with similar activation coefficient K(1/2) (6 and 12 pM, respectively). Jv increased linearly according to the osmotic gradient across the monolayer. A small but highly significant Jv was also measured under isoosmotic conditions. To test the coupling between sodium reabsorption and water flow, mCCD(c11) cells were treated for 24 h under isoosmotic condition with either diluent, amiloride, vasopressin or vasopressin and amiloride. Isc, Jv, and net chemical sodium fluxes were measured across the same monolayers. Around 30% of baseline and 50% of vasopressin-induced water flow is coupled to an amiloride-sensitive, ENaC-mediated, electrogenic sodium transport, whereas the remaining flow is coupled to an amiloride-insensitive, nonelectrogenic sodium transport mediated by an unknown electroneutral transporter. The mCCD(c11) cell line is a first example of a mammalian tight epithelium allowing quantitative study of the coupling between sodium and water transport. Our data are consistent with the 'near isoosmotic' fluid transport model.

Intrauterine growth restriction and absent or reverse end-diastolic blood flow in umbilical artery (Doppler class II or III): A retrospective study of short- and long-term fetal morbidity and mortality.

OBJECTIVE: Absent or reverse end-diastolic flow (Doppler II/III) in umbilical artery is correlated with poor perinatal outcome, particularly in intrauterine growth restricted (IUGR) fetuses. The optimal timing of delivery is still controversial. We studied the short- and long-term morbidity and mortality among these children associated with our defined management. STUDY DESIGN: Sixty-nine IUGR fetuses with umbilical Doppler II/III were divided into three groups; Group 1, severe early IUGR, no therapeutic intervention (n = 7); Group 2, fetuses with pathological biophysical profile, immediate delivery (n = 35); Group 3, fetuses for which expectant management had been decided (n = 27). RESULTS: In Group 1, stillbirth was observed after a mean delay of 6.3 days. Group 2 delivered at an average of 31.6 weeks and two died in the neonatal period (6%). In Group 3 after a mean delay of 8 days, average gestational age at delivery was 31.7 weeks; two intra uterine and four perinatal deaths were observed (22%). Long-term follow-up revealed no sequelae in 25/31 (81%) and 15/18 (83%), and major handicap occurred in 1 (3%) and 2 patients (11%), respectively, for Groups 2 and 3. CONCLUSION: Fetal mortality was observed in 22% of this high risk group. After a mean period of follow-up of 5 years, 82% of infants showed no sequelae. According to our management, IUGR associated with umbilical Doppler II or III does not show any benefit from an expectant management in term of long-term morbidity.

Gene-flow in a mosaic hybrid zone: is local introgression adaptive?

Genome-wide scans of genetic differentiation between hybridizing taxa can identify genome regions with unusual rates of introgression. Regions of high differentiation might represent barriers to gene flow, while regions of low differentiation might indicate adaptive introgression-the spread of selectively beneficial alleles between reproductively isolated genetic backgrounds. Here we conduct a scan for unusual patterns of differentiation in a mosaic hybrid zone between two mussel species, Mytilus edulis and M. galloprovincialis. One outlying locus, mac-1, showed a characteristic footprint of local introgression, with abnormally high frequency of edulis-derived alleles in a patch of M. galloprovincialis enclosed within the mosaic zone, but low frequencies outside of the zone. Further analysis of DNA sequences showed that almost all of the edulis allelic diversity had introgressed into the M. galloprovincialis background in this patch. We then used a variety of approaches to test the hypothesis that there had been adaptive introgression at mac-1. Simulations and model fitting with maximum-likelihood and approximate Bayesian computation approaches suggested that adaptive introgression could generate a "soft sweep," which was qualitatively consistent with our data. Although the migration rate required was high, it was compatible with the functioning of an effective barrier to gene flow as revealed by demographic inferences. As such, adaptive introgression could explain both the reduced intraspecific differentiation around mac-1 and the high diversity of introgressed alleles, although a localized change in barrier strength may also be invoked. Together, our results emphasize the need to account for the complex history of secondary contacts in interpreting outlier loci.

Phylogeographical structure, postglacial recolonization and barriers to gene flow in the distinctive Valais chromosome race of the common shrew (Sorex araneus).

Using one male-inherited and eight biparentally inherited microsatellite markers, we investigate the population genetic structure of the Valais chromosome race of the common shrew (Sorex araneus) in the Central Alps of Europe. Unexpectedly, the Y-chromosome microsatellite suggests nearly complete absence of male gene flow among populations from the St-Bernard and Simplon regions (Switzerland). Autosomal markers also show significant genetic structuring among these two geographical areas. Isolation by distance is significant and possible barriers to gene flow exist in the study area. Two different approaches are used to better understand the geographical patterns and the causes of this structuring. Using a principal component analysis for which testing procedure exists, and partial Mantel tests, we show that the St-Bernard pass does not represent a significant barrier to gene flow although it culminates at 2469 m, close to the highest altitudinal record for this species. Similar results are found for the Simplon pass, indicating that both passes represented potential postglacial recolonization routes into Switzerland from Italian refugia after the last Pleistocene glaciations. In contrast with the weak effect of these mountain passes, the Rhône valley lowlands significantly reduce gene flow in this species. Natural obstacles (the large Rhône river) and unsuitable habitats (dry slopes) are both present in the valley. Moreover, anthropogenic changes to landscape structures are likely to have strongly reduced available habitats for this shrew in the lowlands, thereby promoting genetic differentiation of populations found on opposite sides of the Rhône valley.

Effects of adrenergic and cholinergic blockade on insulin-induced stimulation of calf blood flow in humans.

Euglycemic hyperinsulinemia stimulates both sympathetic nerve activity and blood flow to skeletal muscle, but the mechanism is unknown. Possible mechanisms that may stimulate muscle blood flow include neural, humoral, or metabolic effects of insulin. To determine whether such insulin-induced vasodilation is modulated by stimulation of adrenergic or cholinergic mechanisms, we obtained, in eight healthy lean subjects, plethysmographic measurements of calf blood flow during 3 h of hyperinsulinemic (1 mU.kg-1.min-1) euglycemic clamp performed alone or during concomitant beta-adrenergic (propranolol infusion), cholinergic (atropine infusion), or alpha-adrenergic (prazosin administration) blockade. Euglycemic hyperinsulinemia alone increased calf blood flow by 38 +/- 10% (means +/- SE) and decreased vascular resistance by 27 +/- 4% (P < 0.01). The principal new observation is that these insulin-induced vasodilatory responses were not attenuated by concomitant propranolol or atropine infusion, nor were they potentiated by prazosin administration. In conclusion, these findings provide evidence that during euglycemic hyperinsulinemia in lean healthy humans stimulation of muscle blood flow is not mediated primarily by beta-adrenergic or cholinergic mechanisms. Furthermore, alpha-adrenergic mechanisms do not markedly limit insulin-induced stimulation of muscle blood flow.

Inbreeding and sex-biased gene flow in the ant Formica exsecta.

The objective of this study was to assess breeding and dispersal patterns of both males and females in a monogyne (a single queen per colony) population of ants. Monogyny is commonly associated with extensive nuptial flights, presumably leading to considerable gene flow over large areas. Opposite to these expectations we found evidence of both inbreeding and sex-biased gene flow in a monogyne population of Formica exsecta. We found a significant degree of population subdivision at a local scale (within islands) for queens (females heading established colonies) and workers, but not for colony fathers (the males mated to the colony queens). However, we found little evidence of population subdivision at a larger scale (among islands). More conclusive support for sex-biased gene flow comes from the analysis of isolation by distance on the largest island, and from assignment tests revealing differences in female and male philopatry. The genetic similarity between pairs of queens decreased significantly when geographical distance increased, demonstrating limited dispersal and isolation by distance in queens. By contrast, we found no such pattern for colony fathers. Furthermore, a significantly greater fraction of colony queens were assigned as having originated from the population of residence, as compared to colony fathers. Inbreeding coefficients were significantly positive for workers, but not for mother queens. The queen-male relatedness coefficient of 0.23 (regression relatedness) indicates that mating occurs between fairly close relatives. These results suggest that some monogyne species of ants have complex dispersal and mating systems that can result in genetic isolation by distance over small geographical scales. More generally, this study also highlights the importance of identifying the relevant scale in analyses of population structure and dispersal.

Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework

The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.

The effect of continuous positive airway pressure on total cerebral blood flow in healthy awake volunteers.

PURPOSE: Continuous positive airway pressure (CPAP) is the gold standard treatment for obstructive sleep apnea. However, the physiologic impact of CPAP on cerebral blood flow (CBF) is not well established. Ultrasound can be used to estimate CBF, but there is no widespread accepted protocol. We studied the physiologic influence of CPAP on CBF using a method integrating arterial diameter and flow velocity (FV) measurements obtained for each vessel supplying blood to the brain. METHODS: FV and lumen diameter of the left and right internal carotid, vertebral, and middle cerebral arteries were measured using duplex Doppler ultrasound with and without CPAP at 15 cm H(2)O, applied in a random order. Transcutaneous carbon dioxide (PtcCO(2)), heart rate (HR), blood pressure (BP), and oxygen saturation were monitored. Results were compared with a theoretical prediction of CBF change based on the effect of partial pressure of carbon dioxide on CBF. RESULTS: Data were obtained from 23 healthy volunteers (mean ± SD; 12 male, age 25.1 ± 2.6 years, body mass index 21.8 ± 2.0 kg/m(2)). The mean experimental and theoretical CBF decrease under CPAP was 12.5 % (p < 0.001) and 11.9 % (p < 0.001), respectively. The difference between experimental and theoretical CBF reduction was not statistically significant (3.84 ± 79 ml/min, p = 0.40). There was a significant reduction in PtcCO(2) with CPAP (p = <0.001) and a significant increase in mean BP (p = 0.0017). No significant change was observed in SaO(2) (p = 0.21) and HR (p = 0.62). CONCLUSION: Duplex Doppler ultrasound measurements of arterial diameter and FV allow for a noninvasive bedside estimation of CBF. CPAP at 15 cm H(2)O significantly decreased CBF in healthy awake volunteers. This effect appeared to be mediated predominately through the hypocapnic vasoconstriction coinciding with PCO(2) level reduction. The results suggest that CPAP should be used cautiously in patients with unstable cerebral hemodynamics.