Manual therapy followed by specific active exercises versus a placebo followed by specific active exercises on the improvement of functional disability in patients with chronic non specific low back pain: a randomized controlled trial.

BACKGROUND: Recent clinical recommendations still propose active exercises (AE) for CNSLBP. However, acceptance of exercises by patients may be limited by pain-related manifestations. Current evidences suggest that manual therapy (MT) induces an immediate analgesic effect through neurophysiologic mechanisms at peripheral, spinal and cortical levels. The aim of this pilot study was first, to assess whether MT has an immediate analgesic effect, and second, to compare the lasting effect on functional disability of MT plus AE to sham therapy (ST) plus AE. METHODS: Forty-two CNSLBP patients without co-morbidities, randomly distributed into 2 treatment groups, received either spinal manipulation/mobilization (first intervention) plus AE (MT group; n = 22), or detuned ultrasound (first intervention) plus AE (ST group; n = 20). Eight therapeutic sessions were delivered over 4 to 8 weeks. Immediate analgesic effect was obtained by measuring pain intensity (Visual Analogue Scale) before and immediately after the first intervention of each therapeutic session. Pain intensity, disability (Oswestry Disability Index), fear-avoidance beliefs (Fear-Avoidance Beliefs Questionnaire), erector spinae and abdominal muscles endurance (Sorensen and Shirado tests) were assessed before treatment, after the 8th therapeutic session, and at 3- and 6-month follow-ups. RESULTS: Thirty-seven subjects completed the study. MT intervention induced a better immediate analgesic effect that was independent from the therapeutic session (VAS mean difference between interventions: -0.8; 95% CI: -1.2 to -0.3). Independently from time after treatment, MT + AE induced lower disability (ODI mean group difference: -7.1; 95% CI: -12.8 to -1.5) and a trend to lower pain (VAS mean group difference: -1.2; 95% CI: -2.4 to -0.30). Six months after treatment, Shirado test was better for the ST group (Shirado mean group difference: -61.6; 95% CI: -117.5 to -5.7). Insufficient evidence for group differences was found in remaining outcomes. CONCLUSIONS: This study confirmed the immediate analgesic effect of MT over ST. Followed by specific active exercises, it reduces significantly functional disability and tends to induce a larger decrease in pain intensity, compared to a control group. These results confirm the clinical relevance of MT as an appropriate treatment for CNSLBP. Its neurophysiologic mechanisms at cortical level should be investigated more thoroughly. TRIAL REGISTRATION: Trial registration number: NCT01496144.

An iterative Multiscale Finite-Volume algorithm converging to the exact solution

The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).

Non-pharmacological interventions for chronic pain in people with spinal cord injury.

BACKGROUND: Chronic pain is frequent in persons living with spinal cord injury (SCI). Conventionally, the pain is treated pharmacologically, yet long-term pain medication is often refractory and associated with side effects. Non-pharmacological interventions are frequently advocated, although the benefit and harm profiles of these treatments are not well established, in part because of methodological weaknesses of available studies. OBJECTIVES: To critically appraise and synthesise available research evidence on the effects of non-pharmacological interventions for the treatment of chronic neuropathic and nociceptive pain in people living with SCI. SEARCH METHODS: The search was run on the 1st March 2011. We searched the Cochrane Injuries Group's Specialised Register, the Cochrane Central Register of Controlled Trials (CENTRAL), MEDLINE (OvidSP), Embase (OvidSP), PsycINFO (OvidSP), four other databases and clinical trials registers. In addition, we manually searched the proceedings of three major scientific conferences on SCI. We updated this search in November 2014 but these results have not yet been incorporated. SELECTION CRITERIA: Randomised controlled trials of any intervention not involving intake of medication or other active substances to treat chronic pain in people with SCI. DATA COLLECTION AND ANALYSIS: Two review authors independently extracted data and assessed risk of bias in the included studies. The primary outcome was any measure of pain intensity or pain relief. Secondary outcomes included adverse events, anxiety, depression and quality of life. When possible, meta-analyses were performed to calculate standardised mean differences for each type of intervention. MAIN RESULTS: We identified 16 trials involving a total of 616 participants. Eight different types of interventions were studied. Eight trials investigated the effects of electrical brain stimulation (transcranial direct current stimulation (tDCS) and cranial electrotherapy stimulation (CES); five trials) or repetitive transcranial magnetic stimulation (rTMS; three trials). Interventions in the remaining studies included exercise programmes (three trials); acupuncture (two trials); self-hypnosis (one trial); transcutaneous electrical nerve stimulation (TENS) (one trial); and a cognitive behavioural programme (one trial). None of the included trials were considered to have low overall risk of bias. Twelve studies had high overall risk of bias, and in four studies risk of bias was unclear. The overall quality of the included studies was weak. Their validity was impaired by methodological weaknesses such as inappropriate choice of control groups. An additional search in November 2014 identified more recent studies that will be included in an update of this review.For tDCS the pooled mean difference between intervention and control groups in pain scores on an 11-point visual analogue scale (VAS) (0-10) was a reduction of -1.90 units (95% confidence interval (CI) -3.48 to -0.33; P value 0.02) in the short term and of -1.87 (95% CI -3.30 to -0.45; P value 0.01) in the mid term. Exercise programmes led to mean reductions in chronic shoulder pain of -1.9 score points for the Short Form (SF)-36 item for pain experience (95% CI -3.4 to -0.4; P value 0.01) and -2.8 pain VAS units (95% CI -3.77 to -1.83; P value < 0.00001); this represented the largest observed treatment effects in the included studies. Trials using rTMS, CES, acupuncture, self-hypnosis, TENS or a cognitive behavioural programme provided no evidence that these interventions reduce chronic pain. Ten trials examined study endpoints other than pain, including anxiety, depression and quality of life, but available data were too scarce for firm conclusions to be drawn. In four trials no side effects were reported with study interventions. Five trials reported transient mild side effects. Overall, a paucity of evidence was found on any serious or long-lasting side effects of the interventions. AUTHORS' CONCLUSIONS: Evidence is insufficient to suggest that non-pharmacological treatments are effective in reducing chronic pain in people living with SCI. The benefits and harms of commonly used non-pharmacological pain treatments should be investigated in randomised controlled trials with adequate sample size and study methodology.

Validation d'une version abrégée du TCI (TCI-56) sur un échantillon de jeunes fumeurs et non-fumeurs

Introduction: The psychobiological seven-factor model proposed by Cloninger et al. (1993) takes into account temperament and character dimensions to describe personality. Four of the dimensions are linked with biological, genetic and neuroanatomic structures, whereas the three other dimensions are related to the degree of individual, social and spiritual development. A study conducted by Wills et al. (1994) with adolescents showed that substance abuse was associated with high scores on Novelty Seeking and low scores on Harm Avoidance and Reward Dependence. The aim of the present study was, firstly, to create a short form of Cloninger's (1993) Temperament and Character Inventory (TCI) and, secondly, to study the impact of nicotine dependence as well as demographic variables on a sample of young adults. Method: We created a short form of the TCI containing 56 items (TCI-56), 8 for each scale. Responses are made on a five-point Likert type scale. A Swiss sample (n=211), of 116 women and 95 men, aged from 15 to 30 years, participated in this study. Our population was divided into a group of 81 smokers and another of 130 non-smokers, according to their scores on the Fagerstörm test for nicotine dependence (1999). Results: The structural validation consisted of two separate factor analysis with varimax rotations, one for the temperamental items, and the other, for the character ones. The first factor analysis conducted on the items of the temperament scales allowed to extract 4 factors explaining 40.7% of the variance. The correlations between factors and scales are the following: r=.71 for Novelty Seeking, r=.69 for Persistence, r=.95 for Harm Avoidance, r=.94 for Reward Dependence. The second factor analysis conducted on the items of the character scales allowed to extract 3 factors explaining 41.5% of the variance. The correlations between factors and scales are the following: r=.94 for Self-Directedness, r=.91 for Cooperativeness and r=.99 for Self-Transcendence. The internal consistencies range from α=.65 to α=.75 for the temperament scales, and from α=.71 to α=.83 for the three character scales. Concerning, the impact of the nicotine dependence, we observed that smokers have significantly higher scores for Novelty seeking, than non-smokers (p=.01). We found no difference for Harm Avoidance and Reward Dependence. Nevertheless, smokers seem to have the tendency to score higher on Transcendence (p=.06). Moreover, people having smoked more than 100 cigarettes in their life have significantly higher scores on this scale (p.04) and the correlation between Transcendence and the Fagerstörm test is significant (r=.19). We also found gender differences: the women (N=116) obtain significantly higher scores for Harm Avoidance (p<.001), for Reward Dependence (p<.001) and for Cooperation (p=.01). We further found a significant correlation between age and Self-Directedness, r=.34. We observed no interaction between gender and smoking or age and smoking on the dimensions of the TCI-56. Discussion: The TCI short form (TCI-56) seems to be a valid and useful inventory to assess personality differences. Confirming the results of others about the relation between addiction and personality, we found that smokers have significantly higher scores for Novelty seeking, than non-smokers. But we were not able to find any significant differences for Harm Avoidance and Reward Dependence. This might be due to our sample that was made of young adults. This study also shows that Transcendence could be an interesting dimension for studies on Tobacco smoking to consider. Concerning the impact of demographic variables, we observed that age and gender have specific and coherent influence on personality.

Folner sequences and finite operators

This article analyzes Folner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70ies. We prove that each essentially hyponormal operator has a proper Folner sequence (i.e. a Folner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper Folner sequence. Moreover, we show that an operator is finite if and only if it has a proper Folner sequence or if it has a non-trivial finite dimensional reducing subspace. We also analyze the structure of operators which have no Folner sequence and give examples of them. For this analysis we introduce the notion of strongly non-Folner operators, which are far from finite block reducible operators, in some uniform sense, and show that this class coincides with the class of non-finite operators.

Methodology for studying the numerical speed of sound in finite differences schemes

The space and time discretization inherent to all FDTD schemesintroduce non-physical dispersion errors, i.e. deviations ofthe speed of sound from the theoretical value predicted bythe governing Euler differential equations. A generalmethodologyfor computing this dispersion error via straightforwardnumerical simulations of the FDTD schemes is presented.The method is shown to provide remarkable accuraciesof the order of 1/1000 in a wide variety of twodimensionalfinite difference schemes.

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

Modeling complex wells with the multi-scale finite-volume method

In this paper, an extension of the multi-scale finite-volume (MSFV) method is devised, which allows to Simulate flow and transport in reservoirs with complex well configurations. The new framework fits nicely into the data Structure of the original MSFV method,and has the important property that large patches covering the whole well are not required. For each well. an additional degree of freedom is introduced. While the treatment of pressure-constraint wells is trivial (the well-bore reference pressure is explicitly specified), additional equations have to be solved to obtain the unknown well-bore pressure of rate-constraint wells. Numerical Simulations of test cases with multiple complex wells demonstrate the ability of the new algorithm to capture the interference between the various wells and the reservoir accurately. (c) 2008 Elsevier Inc. All rights reserved.

The effects of physiologically plausible connectivity structure on local and global dynamics in large scale brain models.

Functionally relevant large scale brain dynamics operates within the framework imposed by anatomical connectivity and time delays due to finite transmission speeds. To gain insight on the reliability and comparability of large scale brain network simulations, we investigate the effects of variations in the anatomical connectivity. Two different sets of detailed global connectivity structures are explored, the first extracted from the CoCoMac database and rescaled to the spatial extent of the human brain, the second derived from white-matter tractography applied to diffusion spectrum imaging (DSI) for a human subject. We use the combination of graph theoretical measures of the connection matrices and numerical simulations to explicate the importance of both connectivity strength and delays in shaping dynamic behaviour. Our results demonstrate that the brain dynamics derived from the CoCoMac database are more complex and biologically more realistic than the one based on the DSI database. We propose that the reason for this difference is the absence of directed weights in the DSI connectivity matrix.

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.

An adaptive multiscale method for density-driven instabilities

Accurate modeling of flow instabilities requires computational tools able to deal with several interacting scales, from the scale at which fingers are triggered up to the scale at which their effects need to be described. The Multiscale Finite Volume (MsFV) method offers a framework to couple fine-and coarse-scale features by solving a set of localized problems which are used both to define a coarse-scale problem and to reconstruct the fine-scale details of the flow. The MsFV method can be seen as an upscaling-downscaling technique, which is computationally more efficient than standard discretization schemes and more accurate than traditional upscaling techniques. We show that, although the method has proven accurate in modeling density-driven flow under stable conditions, the accuracy of the MsFV method deteriorates in case of unstable flow and an iterative scheme is required to control the localization error. To avoid large computational overhead due to the iterative scheme, we suggest several adaptive strategies both for flow and transport. In particular, the concentration gradient is used to identify a front region where instabilities are triggered and an accurate (iteratively improved) solution is required. Outside the front region the problem is upscaled and both flow and transport are solved only at the coarse scale. This adaptive strategy leads to very accurate solutions at roughly the same computational cost as the non-iterative MsFV method. In many circumstances, however, an accurate description of flow instabilities requires a refinement of the computational grid rather than a coarsening. For these problems, we propose a modified iterative MsFV, which can be used as downscaling method (DMsFV). Compared to other grid refinement techniques the DMsFV clearly separates the computational domain into refined and non-refined regions, which can be treated separately and matched later. This gives great flexibility to employ different physical descriptions in different regions, where different equations could be solved, offering an excellent framework to construct hybrid methods.

A non-linear Bayesian approach for upscaling local-scale hydraulic conductivity measurements based on local- and regional-scale geophysical data

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the regional scale represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed an upscaling procedure based on a Bayesian sequential simulation approach. This method is then applied to the stochastic integration of low-resolution, regional-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities. Finally, the overall viability of this upscaling approach is tested and verified by performing and comparing flow and transport simulation through the original and the upscaled hydraulic conductivity fields. Our results indicate that the proposed procedure does indeed allow for obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.