Leray and LANS-α\alpha modeling of turbulent mixing

Mathematical regularisation of the nonlinear terms in the Navier-Stokes equations provides a systematic approach to deriving subgrid closures for numerical simulations of turbulent flow. By construction, these subgrid closures imply existence and uniqueness of strong solutions to the corresponding modelled system of equations. We will consider the large eddy interpretation of two such mathematical regularisation principles, i.e., Leray and LANS$-\alpha$ regularisation. The Leray principle introduces a {\bfi smoothed transport velocity} as part of the regularised convective nonlinearity. The LANS$-\alpha$ principle extends the Leray formulation in a natural way in which a {\bfi filtered Kelvin circulation theorem}, incorporating the smoothed transport velocity, is explicitly satisfied. These regularisation principles give rise to implied subgrid closures which will be applied in large eddy simulation of turbulent mixing. Comparison with filtered direct numerical simulation data, and with predictions obtained from popular dynamic eddy-viscosity modelling, shows that these mathematical regularisation models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure

Modeling and simulation of phase-transitions in multicomponent aluminum alloy casting

The casting process of aluminum products involves the spatial distribution of alloying elements. It is essential that these elements are uniformly distributed in order to guarantee reliable and consistent products. This requires a good understanding of the main physical mechanisms that affect the solidification, in particular the thermodynamic description and its coupling to the transport processes of heat and mass that take place. The continuum modeling is reviewed and methods for handling the thermodynamics component of multi-element alloys are proposed. Savings in data-storage and computing costs on the order of 100 or more appear possible, when a combination of data-reduction and data-representation methods is used. To test the new approach a simplified model was proposed and shown to qualitatively capture the evolving solidification front

On the Clark-alpha model of turbulence: global regularity and long--time dynamics

In this paper we study a well-known three--dimensional turbulence model, the filtered Clark model, or Clark-alpha model. This is Large Eddy Simulation (LES) tensor-diffusivity model of turbulent flows with an additional spatial filter of width alpha ($\alpha$). We show the global well-posedness of this model with constant Navier-Stokes (eddy) viscosity. Moreover, we establish the existence of a finite dimensional global attractor for this dissipative evolution system, and we provide an anaytical estimate for its fractal and Hausdorff dimensions. Our estimate is proportional to $(L/l_d)^3$, where $L$ is the integral spatial scale and $l_d$ is the viscous dissipation length scale. This explicit bound is consistent with the physical estimate for the number of degrees of freedom based on heuristic arguments. Using semi-rigorous physical arguments we show that the inertial range of the energy spectrum for the Clark-$\aa$ model has the usual $k^{-5/3}$ Kolmogorov power law for wave numbers $k\aa \ll 1$ and $k^{-3}$ decay power law for $k\aa \gg 1.$ This is evidence that the Clark$-\alpha$ model parameterizes efficiently the large wave numbers within the inertial range, $k\aa \gg 1$, so that they contain much less translational kinetic energy than their counterparts in the Navier-Stokes equations.Comment: 11 pages, no figures, submitted to J of Turbulenc

Acid-base changes and acetate metabolism during routine and high-efficiency hemodialysis in children

Acid-base changes and acetate metabolism during routine and high-efficiency hemodialysis in children. Changes in acid-base status and plasma acetate concentrations were studied in eight children during 11 hemodialysis sessions. During dialysis, the blood bicarbonate concentration fell (20.5 ± 0.7 to 19.6 ± 0.8 mEq/liter), the PCO2 fell (33.4 ± 0.8 to 27.5 ± 1.4 mm Hg), and the pH rose (7.42 ± 0.01 to 7.48 ± 0.02). During the hour after dialysis, the bicarbonate concentration rose to normal (23.4 ± 0.7 mEq/liter), the PCO2 rose (32.8 ± 0.8 mm Hg), and the pH remained unchanged. The half-life of plasma acetate, measured after dialysis, was 8.7 min. During five “high-efficiency” dialysis sessions (urea clearance, > 3.0 ml/min/kg), blood bicarbonate concentration fell 3.2 mEq/liter, PCO2 fell 8.7 mm Hg, and plasma acetate rose to 7.51 mmoles/liter, whereas during six “routine efficiency” dialysis sessions (urea clearance, 1.5 to 3.0 ml/min/kg), blood bicarbonate rose 1.0 mEq/liter, PCO2 fell 36 mm Hg, and plasma acetate rose to 3.52 mmoles/liter. At 1 hour after the end of dialysis, blood bicarbonate, PCO2, and plasma acetate concentrations were similar in the two groups. Clinical problems occurred more frequently in the high-efficiency group during dialysis although the difference was not significant. The data indicate that (1) dialysis with acetate buffer effectively corrects pre-dialysis metabolic acidosis, (2) although children have a high rate of acetate metabolism, during high-efficiency dialysis this rate is exceeded by the influx of acetate, and acid-base abnormalities occur. These abnormalities are transient but may cause clinical problems.Modifications acido-basiques et métabolisme de l'acétate au cours de l'hémodialyse de routine ou à efficacité élevée chez l'enfant. Les modifications de l'état acido-basique et des concentrations plasmatiques d'acétate ont été étudiées chez huit enfants au cours de 11 séances d'hémodialyse. Au cours de la dialyse les bicarbonates diminuent (20,5 ± 0,7 à 19,6 ± 0,8 mEq/ litre), la PCO2 diminue (33,4 ± 0,8 à 27,5 ± 1,4 mm Hg), et le pH augmente (7,42 ± 0,01 à 7,48 ± 0,02). Au cours de l'heure qui suit la dialyse les bicarbonates s'élèvent à une valeur normale, 23,4 ± 0,07 mEq/litre, la PCO2 s'élève à 32,8 ± 0,8 mm Hg, et le pH est inchangé. La demi vie de l'acétate plasmatique, mesurée après la dialyse, était de 8,7 min. Au cours de cinq séances de dialyse à haute efficacité (clearance de l'urée, > 3,0 ml/min/kg) les bicarbonates baissent de 3,2 mEq/litre, la PCO2 de 8,7 mm Hg, et l'acétate plasmatique s'est élevé à 7,51 mmoles/litre alors qu'au cours de six séances de dialyse d'efficacité moyenne (clearance de l'urée, 1,5 à 3,0 ml/min/kg) les bicarbonates ont augmenté de 1,0 mEq/litre, la PCO2 a diminué de 3,6 mm Hg, et l'acétate plasmatique s'est élevé à 3,52 mmoles/litre. Une heure après la fin de la dialyse les bicarbonates, la PCO2 et l'acétate plasmatique étaient semblables dans les deux groupes. Des problèmes cliniques sont survenus plus souvent au cours de la dialyse dans le groups à haute efficacité bien que la différence ne soit pas significative. Ces résultats indiquent que (1) la dialyse avec le tampon acétate corrige efficacement l'acidose métabolique pré-dialytique, (2) bien que l'enfant ait une capacité élevée de métaboliser l'acétate, cette capacité est débordée, au cours de la dialyse à haute efficacité, par l'entrée d'acétate et des anomalies acidobasiques surviennent. Ces anomalies sont transitoires et peuvent déterminer des problèmes cliniques

When Does Eddy Viscosity Damp Subfilter Scales Sufficiently?

Large eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. The very essence is that the LES-solution contains only scales of size ≥Δ, where Δ denotes some user-chosen length scale. This property enables us to perform a LES when it is not feasible to compute the full, turbulent solution of the Navier-Stokes equations. Therefore, in case the large eddy simulation is based on an eddy viscosity model we determine the eddy viscosity such that any scales of size <Δ are dynamically insignificant. In this paper, we address the following two questions: how much eddy diffusion is needed to (a) balance the production of scales of size smaller than Δ; and (b) damp any disturbances having a scale of size smaller than Δ initially. From this we deduce that the eddy viscosity νe has to depend on the invariants q = ½tr(S^2) and r =−⅓tr(S^3) of the (filtered) strain rate tensor S. The simplest model is then given by νe = 3/2(Δ/π)^2|r|/q. This model is successfully tested for a turbulent channel flow (Reτ = 590).

Increasing the information provided by probabilistic sensitivity analysis:The relative density plot

Background Results of probabilistic sensitivity analyses (PSA) are frequently visualized as a scatterplot, which is limited through overdrawing and a lack of insight in relative density. To overcome these limitations, we have developed the Relative Density plot (PSA-ReD). Methods The PSA-ReD combines a density plot and a contour plot to visualize and quantify PSA results. Relative density, depicted using a color gradient, is transformed to a cumulative probability. Contours are then plotted over regions with a specific cumulative probability. We use two real-world case studies to demonstrate the value of the PSA-ReD plot. Results The PSA-ReD method demonstrates proof-of-concept and feasibility. In the real-world case-studies, PSA-ReD provided additional visual information that could not be understood from the traditional scatterplot. High density areas were identified by color-coding and the contour plot allowed for quantification of PSA iterations within areas of the cost-effectiveness plane, diminishing overdrawing and putting infrequent iterations in perspective. Critically, the PSA-ReD plot informs modellers about non-linearities within their model. Conclusions The PSA-ReD plot is easy to implement, presents more of the information enclosed in PSA data, and prevents inappropriate interpretation of PSA results. It gives modelers additional insight in model functioning and the distribution of uncertainty around the cost-effectiveness estimate

Reported Challenges in Health Technology Assessment of Complex Health Technologies

Objectives: With complex health technologies entering the market, methods for health technology assessment (HTA) may require changes. This study aimed to identify challenges in HTA of complex health technologies.  Methods: A survey was sent to European HTA organizations participating in European Network for HTA (EUnetHTA). The survey contained open questions and used predefined potentially complex health technologies and 7 case studies to identify types of complex health technologies and challenges faced during HTA. The survey was validated, tested for reliability by an expert panel, and pilot tested before dissemination.  Results: A total of 22 HTA organizations completed the survey (67%). Advanced therapeutic medicinal products (ATMPs) and histology-independent therapies were considered most challenging based on the predefined complex health technologies and case studies. For the case studies, more than half of the reported challenges were “methodological,” equal in relative effectiveness assessments as in cost-effectiveness assessments. Through the open questions, we found that most of these challenges actually rooted in data unavailability. Data were reported as “absent,” “insufficient,” “immature,” or “low quality” by 18 of 20 organizations (90%), in particular data on quality of life. Policy and organizational challenges and challenges because of societal or political pressure were reported by 8 (40%) and 4 organizations (20%), respectively. Modeling issues were reported least often (n = 2, 4%).  Conclusions: Most challenges in HTA of complex health technologies root in data insufficiencies rather than in the complexity of health technologies itself. As the number of complex technologies grows, the urgency for new methods and policies to guide HTA decision making increases

Real World Data in Health Technology Assessment of Complex Health Technologies

The available evidence on relative effectiveness and risks of new health technologies is often limited at the time of health technology assessment (HTA). Additionally, a wide variety in real-world data (RWD) policies exist among HTA organizations. This study assessed which challenges, related to the increasingly complex nature of new health technologies, make the acceptance of RWD most likely. A questionnaire was disseminated among 33 EUnetHTA member HTA organizations. The questions focused on accepted data sources, circumstances that allowed for RWD acceptance and barriers to acceptance. The questionnaire was validated and tested for reliability by an expert panel, and pilot-tested before dissemination via LimeSurvey. Twenty-two HTA organizations completed the questionnaire (67%). All reported accepting randomized clinical trials. The most accepted RWD source were patient registries (19/22, 86%), the least accepted were editorials and expert opinions (8/22, 36%). With orphan treatments or companion diagnostics, organizations tended to be most likely to accept RWD sources, 4.3-3.2 on a 5-point Likert scale, respectively. Additional circumstances were reported to accept RWD (e.g., a high disease burden). The two most important barriers to accepting RWD were lacking necessary RWD sources and existing policy structures. European HTA organizations seem positive toward the (wider) use of RWD in HTA of complex therapies. Expanding the use of patient registries could be potentially useful, as a large share of the organizations already accepts this source. However, many barriers still exist to the widespread use of RWD. Our results can be used to prioritize circumstances in which RWD might be accepted