Behavior of upwind scheme in the low Mach number limit : III. Preconditioned dissipation for a five equation two phase model

For single phase fluid models, like the Euler equations of compressible gas dynamics, upwind finite volume schemes suffer from a loss of accuracy when computing flows in the near incompressible regime. Preconditioning of the numerical dissipation is necessary to recover results consistent with the asymptotic behaviour of the continuous model. In this paper, we examine this situation for a two phase flow model. We show that as in the single phase case, the numerical approximation has to be done carefully in the near incompressible regime. We propose to adapt the preconditioning strategy used for single phase problems and present numerical results that show the efficiency of this approac

On the Behavior of Upwind Schemes in the Low Mach Number Limit: II. Godunov Type Schemes

This paper presents an analysis of Godunov scheme in the low Mach number regime. We study the Riemann problem and show that the interface pressure contains acoustic waves of order Mach even if the initial data are well prepared and contain only pressure fluctuations of order Mach squared. We then propose to modify the fluxes computed by Godunov type schemes by solving a preconditioned Riemann problem instead of the original one. This strategy is applied to VFRoe solvers where we show that it allows to recover a correct scaling of the pressure fluctuations. Numerical experimen- ts confirm these theoretical results

A five equation reduced Model for compressible two phase flow problems

This paper presents an Euleriean model for the simulation of compressible two-phase flow problems. The starting point of the study is a seven equation, two pressure, two velocity model. This model contains relaxation terms that drive the systems toward pressure and velocity equilibrium. We perform an asymptotic analysis of this system in the limit of zero relaxation time and derive a five equation hyperbolic reduced system. We study the mathematical properties of the system, the structure of the waves and the expression of the Riemann's invariants. We then describe two different numerical approximation schemes for this system. The first one relies on a linearized Riemann solver while the second uses more heavily the mathematical structure of the system and relies on a linearization of the characteristic relations. Finally, we present some numerical experiments and comparison with the results obtained by the two pressure, two velocity model as well as some test cases in interface computations

Behavior of upwind scheme in the low Mach number limit : III. Preconditioned dissipation for a five equation two phase model

For single phase fluid models, like the Euler equations of compressible gas dynamics, upwind finite volume schemes suffer from a loss of accuracy when computing flows in the near incompressible regime. Preconditioning of the numerical dissipation is necessary to recover results consistent with the asymptotic behaviour of the continuous model. In this paper, we examine this situation for a two phase flow model. We show that as in the single phase case, the numerical approximation has to be done carefully in the near incompressible regime. We propose to adapt the preconditioning strategy used for single phase problems and present numerical results that show the efficiency of this approac

Seven-equation, two-phase flow three-dimensional calculations using a Mixed-Element-Volume method

We present the extension of the five-equation two-dimensional two-phase model of Guillard and Murrone to three-dimensions. The Riemann solver is the acoustic version of the one proposed by Guillard and Murrone. The numerical scheme is a Mixed-Element-Volume approximation centered on the vertices of a tetrahedrization. It uses an edge based formulation. Upstream-Downstream tetrahedra-based limiters are applied for positiveness reinforcement. The computation in advanced in time using explicit multi-stage schemes. This numerical technology is implemented in the parallel mode using mesh partitioning and the message passing interface (MPI). We present some preliminary computations for validation with respect to 2D results and an application to the action of a blast wave on a dense bubble

ANALYSE DE SENSIBILITÉ DE LA DISPERSION DE GOUTTELETTES AUX CONDITIONS D'ÉMISSION ET A L'AIR AMBIENT

National audienceThis work presents a methodology to analyse the sensitivity of numerical simulations related to the dispersion of droplets in the air. The methodology is based on existing tools for sensitivity analysis (e.g. Sobol sensitivity index). This methodology is illustrated by analysing a large number of numerical results obtained in two situations: first a simple toy model (without underlying flow) and then a more realistic case (with underlying flow). The preliminary results allow to identify the parameters affecting the results but show a significant impact of the observable chosen for the analysis.Nous présentons une méthodologie pour analyser la sensibilité et quantifier l'incertitude des résultats de simulation numérique obtenus dans le contexte de la dispersion de gouttelettes dans l'air. La méthodologie se fonde sur les outils existants d'analyse de sensibilité (notamment la méthode de Sobol). L'intérêt de recourir à ces outils d'analyse de grands nombres de résultats est illustré à travers deux situations: un cas simplifié sans écoulement fluide environnant et un cas réaliste avec écoulement fluide. Les résultats préliminaires permettent d'identifier les paramètres influençant les résultats numériques mais montrent une forte sensibilité à l'observable choisie pour l'analyse

Associations between depressive symptoms and disease progression in older patients with chronic kidney disease: results of the EQUAL study

Background Depressive symptoms are associated with adverse clinical outcomes in patients with end-stage kidney disease; however, few small studies have examined this association in patients with earlier phases of chronic kidney disease (CKD). We studied associations between baseline depressive symptoms and clinical outcomes in older patients with advanced CKD and examined whether these associations differed depending on sex. Methods CKD patients (>= 65 years; estimated glomerular filtration rate <= 20 mL/min/1.73 m(2)) were included from a European multicentre prospective cohort between 2012 and 2019. Depressive symptoms were measured by the five-item Mental Health Inventory (cut-off <= 70; 0-100 scale). Cox proportional hazard analysis was used to study associations between depressive symptoms and time to dialysis initiation, all-cause mortality and these outcomes combined. A joint model was used to study the association between depressive symptoms and kidney function over time. Analyses were adjusted for potential baseline confounders. Results Overall kidney function decline in 1326 patients was -0.12 mL/min/1.73 m(2)/month. A total of 515 patients showed depressive symptoms. No significant association was found between depressive symptoms and kidney function over time (P = 0.08). Unlike women, men with depressive symptoms had an increased mortality rate compared with those without symptoms [adjusted hazard ratio 1.41 (95% confidence interval 1.03-1.93)]. Depressive symptoms were not significantly associated with a higher hazard of dialysis initiation, or with the combined outcome (i.e. dialysis initiation and all-cause mortality). Conclusions There was no significant association between depressive symptoms at baseline and decline in kidney function over time in older patients with advanced CKD. Depressive symptoms at baseline were associated with a higher mortality rate in men

Modèles bi-fluides à six et sept équations pour les écoulements diphasiques à faible nombre de Mach

This thesis deals with the study of models and numerical methods for low Mach number compressible two phase flows. All numerical methods developed in this study are based on finite volume formulation for unstructured mesh. The first part of the thesis propose an analysis of the behavior of upwind Godunov type schemes in the low Mach number limit. We explain the reasons why these schemes give unaccurate approximations when the flows are near the incompressible limit. We consequently develop preconditioning methods which allow to recover good approximations. This first part of the study complete several recent works on the analysis of upwind schemes in the low Mach number limit. The second part of the thesis deals with a modelling work where we derive a five equation reduced model for compressible two phase flows, starting from a seven equation model which is a slight variation of the original Baer-Nunziato model. This work presents an original method to reduce hyperbolic systems with stiff source terms. We develop for this model an implicit numerical scheme and following the strategy of the first part of the thesis, a preconditioning method for low Mach number flows. With respect to the numerical test we have realized, the model seems very suitable to compute detonations waves and also for the simulation of interfaces between compressible fluids. Finally, we develop for a seven equation model, a numerical implicit scheme based on approximate Riemann solvers, which allows to reduce the cost of the computations of low Mach number two phase flows.Cette thèse porte sur l'étude de modèles et de méthodes numériques pour les écoulements diphasiques compressibles à faible nombre de Mach. Toutes les méthodes numériques développées dans cette étude sont basées sur une formulation de type volumes finis en maillages non structurés. La première partie de cette thèse propose une analyse du comportement des schémas décentrés de type Godunov dans la limite des faibles nombres de Mach. Nous expliquons de manière rigoureuse les raisons pour lesquelles ces schémas aboutissent à des approximations imprécises lorsque les écoulements sont très proches de l'incompressible. Nous développons alors des méthodes de préconditionnement adaptées qui permettent de retrouver de bonnes approximations. Ce premier travail complète un certain nombre de travaux récents sur l'analyse des schémas décentrés dans la limite des faibles nombres de Mach. Le deuxième point abordé dans cette thèse est un travail de modélisation où nous développons à partir d'un modèle bi-fluides à sept équations de type Baer-Nunziato, un modèle réduit à cinq équations pour les écoulements diphasiques. Ce travail présente une méthode originale de réduction de systèmes hyperboliques avec termes sources raides. Nous développons pour ce modèle un schéma numérique implicite et suivant la stratégie utilisée dans la première partie de cette thèse, une technique de préconditionnement adaptée aux écoulements à faible vitesse. Les expériences numériques réalisées montrent que ce modèle est bien adapté au calcul d'ondes de détonations ainsi qu'à la simulation d'interfaces entre fluides compressibles. Enfin la dernière partie de cette thèse porte sur l'étude d'un modèle à sept équations pour le calcul d'écoulements diphasiques à faible nombre de Mach. On développe des méthodes numériques implicites basées sur des solveurs de Riemann approchés, permettant de réduire les coûts de calcul pour ce type de régime

A five equation reduced model for compressible two phase flow problems

International audienceThis paper studies an Eulerian diffuse interface model for the simulation of compressible multifluid and two-phase flow problems. We first show how to derive this model from a seven equation, two pressure, two velocity model of Baer-Nunziato type using an asymptotic analysis in the limit of zero relaxation time. We then study the mathematical properties of the system, the structure of the waves, the expression of the Riemann's invariants and the existence of a mathematical entropy. We also describe two different numerical approximation schemes for this system. The first one relies on a linearized Riemann solver while the second uses more heavily the mathematical structure of the system and relies on a linearization of the characteristic relations. Finally, we present some numerical experiments and comparisons with the results obtained by the two pressure, two velocity model as well as some test cases and comparisons with another five equation model recently proposed for interface computations between compressible fluids