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T. Tachim Medjo - One of the best experts on this subject based on the ideXlab platform.
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Large deviation for a 2D Cahn-Hilliard-Navier-Stokes Model under random influences
Journal of Mathematical Analysis and Applications, 2020Co-Authors: G. Deugoué, T. Tachim MedjoAbstract:Abstract In this article, we derive a large deviation principle for a 2D Cahn-Hilliard-Navier-Stokes Model under random influences. The Model consists of the Navier-Stokes equations for the velocity, coupled with a Cahn-Hilliard equation for the order (phase) parameter. The proof relies on the weak convergence method that was introduced in [3] , [4] , [5] and based on a variational representation on infinite-dimensional Brownian motion.
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On the weak solutions to a 3D stochastic Cahn–Hilliard–Navier–Stokes Model
Zeitschrift für angewandte Mathematik und Physik, 2019Co-Authors: T. Tachim MedjoAbstract:We study in this article a stochastic version of a coupled Cahn–Hilliard–Navier–Stokes Model in a two- or three-dimensional bounded domain. The Model consists of the Navier–Stokes equations for the velocity, coupled with an Cahn–Hilliard Model for the order (phase) parameter. We prove the existence of a probabilistic weak solution. The proof relies on a Galerkin approximation as well as some compactness results. In the two-dimensional case, we also derive the uniqueness of the weak solutions.
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On the existence and uniqueness of solution to a stochastic 2D Allen–Cahn–Navier–Stokes Model
Stochastics and Dynamics, 2019Co-Authors: T. Tachim MedjoAbstract:We study, in this paper, a stochastic version of a coupled Allen–Cahn–Navier–Stokes Model in a two-dimensional (2D) bounded domain. The Model consists of the Navier–Stokes equations (NSEs) for the ...
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On the existence and uniqueness of solution to a stochastic 2D Allen–Cahn–Navier–Stokes Model
Stochastics and Dynamics, 2019Co-Authors: T. Tachim MedjoAbstract:We study, in this paper, a stochastic version of a coupled Allen–Cahn–Navier–Stokes Model in a two-dimensional (2D) bounded domain. The Model consists of the Navier–Stokes equations (NSEs) for the velocity, coupled with a Allen–Cahn Model for the order (phase) parameter. We prove the existence and the uniqueness of a variational solution.
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The exponential behavior of a stochastic Cahn-Hilliard-Navier-Stokes Model with multiplicative noise
Communications on Pure & Applied Analysis, 2019Co-Authors: T. Tachim MedjoAbstract:In this article, we study the stability of weak solutions to a stochastic version of a coupled Cahn-Hilliard-Navier-Stokes Model with multiplicative noise. The Model consists of the Navier-Stokes equations for the velocity, coupled with an Cahn-Hilliard Model for the order (phase) parameter. We prove that under some conditions on the forcing terms, the weak solutions converge exponentially in the mean square and almost surely exponentially to the stationary solutions. We also prove a result related to the stabilization of these equations.
Sebastian Minjeaud - One of the best experts on this subject based on the ideXlab platform.
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an unconditionally stable uncoupled scheme for a triphasic cahn hilliard navier Stokes Model
Numerical Methods for Partial Differential Equations, 2013Co-Authors: Sebastian MinjeaudAbstract:We propose an original scheme for the time discretization of a triphasic Cahn- Hilliard/Navier-Stokes Model. This scheme allows an uncoupled resolution of the discrete Cahn-Hilliard and Navier-Stokes system, is unconditionally stable and preserves, at the discrete level, the main properties of the continuous Model. The existence of discrete solutions is proved and a convergence study is performed in the case where the densities of the three phases are the same.
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An unconditionally stable uncoupled scheme for a triphasic Cahn-Hilliard/Navier-Stokes Model
Numerical Methods for Partial Differential Equations, 2013Co-Authors: Sebastian MinjeaudAbstract:We propose an original scheme for the time discretization of a triphasic Cahn- Hilliard/Navier-Stokes Model. This scheme allows an uncoupled resolution of the discrete Cahn-Hilliard and Navier-Stokes system, is unconditionally stable and preserves, at the discrete level, the main properties of the continuous Model. The existence of discrete solutions is proved and a convergence study is performed in the case where the densities of the three phases are the same.
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An unconditionally stable uncoupled scheme for a triphasic Cahn–Hilliard/Navier–Stokes Model
Numerical Methods for Partial Differential Equations, 2012Co-Authors: Sebastian MinjeaudAbstract:We propose an original scheme for the time discretization of a triphasic Cahn- Hilliard/Navier-Stokes Model. This scheme allows an uncoupled resolution of the discrete Cahn-Hilliard and Navier-Stokes system, is unconditionally stable and preserves, at the discrete level, the main properties of the continuous Model. The existence of discrete solutions is proved and a convergence study is performed in the case where the densities of the three phases are the same.
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An unconditionally stable uncoupled scheme for the approximation of a triphasic Cahn-Hilliard/Navier-Stokes Model
2011Co-Authors: Sebastian MinjeaudAbstract:We propose an original scheme for the time discretization of a triphasic Cahn-Hilliard/Navier-Stokes Model. This scheme allows an uncoupled resolution of the discrete Cahn-Hilliard and Navier-Stokes system, is unconditionally stable and preserves, at the discrete level, the main properties of the continuous Model. The existence of discrete solution is proved and a convergence study is performed in the case where the densities of the three phases are the same.
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cahn hilliard navier Stokes Model for the simulation of three phase flows
Transport in Porous Media, 2010Co-Authors: Franck Boyer, Sebastian Minjeaud, Celine Lapuerta, Bruno Piar, Michel QuintardAbstract:In this article, we describe some aspects of the diffuse interface Modelling of incompressible flows, composed of three immiscible components, without phase change. In the diffuse interface methods, system evolution is driven by the minimisation of a free energy. The originality of our approach, derived from the Cahn–Hilliard Model, comes from the particular form of energy we proposed in Boyer and Lapuerta (M2AN Math Model Numer Anal, 40:653–987,2006), which, among other interesting properties, ensures consistency with the two-phase Model. The Modelling of three-phase flows is further completed by coupling the Cahn–Hilliard system and the Navier–Stokes equations where surface tensions are taken into account through volume capillary forces. These equations are discretized in time and space paying attention to the fact that most of the main properties of the original Model (volume conservation and energy estimate) have to be maintained at the discrete level. An adaptive refinement method is finally used to obtain an accurate resolution of very thin moving internal layers, while limiting the total number of cells in the grids all along the simulation. Different numerical results are given, from the validation case of the lens spreading between two phases (contact angles and pressure jumps), to the study of mass transfer through a liquid/liquid interface crossed by a single rising gas bubble. The numerical applications are performed with large ratio between densities and viscosities and three different surface tensions.
Steinar Evje - One of the best experts on this subject based on the ideXlab platform.
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A general cell–fluid Navier–Stokes Model with inclusion of chemotaxis
Mathematical Models and Methods in Applied Sciences, 2020Co-Authors: Yangyang Qiao, Steinar EvjeAbstract:The main purpose of this work is to explore a general cell–fluid Model which is based on a mixture theory formulation that accounts for the interplay between oxytactically (chemotaxis toward gradient in oxygen) moving bacteria cells in water and the buoyance forces caused by the difference in density between cells and fluid. The Model involves two mass balance and two general momentum balance equations, respectively, for the cell and fluid phase, combined with a convection–diffusion–reaction equation for oxygen. In particular, the momentum balance equations include interaction terms which describe the cell–fluid drag force effect. Hence, the Model is an extension of the classical Navier–Stokes equation in two different ways: (i) inclusion of two phases (cell and fluid) instead of one; (ii) inclusion of a chemotactic transport mechanism. The Model can be understood as a natural generalization of the much studied chemotaxis-Stokes Model explored by [I. Tuval, L. Cisneros, C. Dombrowski, C. W. Wolgemuth, J. O. Kessler and R. E. Goldstein, Bacterial swimming and oxygen transport near contact lines, Proc. Natl. Acad. Sci. USA 102 (2005) 2277–2282]. First, we explore the Model for parameters in a range which ensures that it lies close to the previously studied chemotaxis-Stokes Model (essentially very low cell volume fraction). Main observations are (i) formation of sinking finger-shaped plumes and (ii) convergence to plumes that possibly can be stationary (i.e. persist over time). The general cell–fluid Model provides new insight into the role played by the cell–fluid interaction term which controls the competition between gravity segregation and chemotaxis effect on the formation of cell plumes. Second, we explore cases with large cell volume fraction (far beyond the regime captured by the chemotaxis-Stokes Model), which gives rise to rich pattern-formation behavior. The general cell–fluid Model opens for exploring a hierarchy of different “subModels”. Hence, it seems to be an interesting Model for further investigations of various, general cell–fluid spatio-temporal evolution dynamics, both from an experimental and mathematical point of view.
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A general cell–fluid Navier–Stokes Model with inclusion of chemotaxis
Mathematical Models and Methods in Applied Sciences, 2020Co-Authors: Yangyang Qiao, Steinar EvjeAbstract:The main purpose of this work is to explore a general cell–fluid Model which is based on a mixture theory formulation that accounts for the interplay between oxytactically (chemotaxis toward gradie...
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weak solutions of a two phase navier Stokes Model with a general slip law
Journal of Functional Analysis, 2015Co-Authors: Steinar EvjeAbstract:Abstract This work is devoted to a study of a gas–liquid Navier–Stokes Model with a general slip law that allows the two phases to flow with unequal fluid velocity. The slip law is general enough to describe counter-current flow, i.e., a situation where gas and liquid move in opposite direction. Motivated by applications in the context of wellbore flow systems we assume that there is a free interface which separates the gas–liquid mixture region from a strongly gas dominated region which holds a specified positive pressure p ⁎ . The slip law is incorporated in the mass and momentum equations resulting in a Model where flow is described in terms of the gas velocity. However, the mixture momentum equation contains a generalized pressure law composed of the standard pressure function combined with three new terms that depend on parameters characterizing the difference between gas and liquid velocity. These new terms make the analysis challenging. By carefully exploiting the positive external pressure p ⁎ we are able to obtain uniform lower and upper bounds on a pressure-related quantity. This in turn allows for various higher order regularity estimates which imply that global existence and uniqueness of weak solutions can be shown.
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Weak solutions of a two-phase Navier–Stokes Model with a general slip law
Journal of Functional Analysis, 2015Co-Authors: Steinar Evje, Huanyao WenAbstract:Abstract This work is devoted to a study of a gas–liquid Navier–Stokes Model with a general slip law that allows the two phases to flow with unequal fluid velocity. The slip law is general enough to describe counter-current flow, i.e., a situation where gas and liquid move in opposite direction. Motivated by applications in the context of wellbore flow systems we assume that there is a free interface which separates the gas–liquid mixture region from a strongly gas dominated region which holds a specified positive pressure p ⁎ . The slip law is incorporated in the mass and momentum equations resulting in a Model where flow is described in terms of the gas velocity. However, the mixture momentum equation contains a generalized pressure law composed of the standard pressure function combined with three new terms that depend on parameters characterizing the difference between gas and liquid velocity. These new terms make the analysis challenging. By carefully exploiting the positive external pressure p ⁎ we are able to obtain uniform lower and upper bounds on a pressure-related quantity. This in turn allows for various higher order regularity estimates which imply that global existence and uniqueness of weak solutions can be shown.
Alvaro Soruco - One of the best experts on this subject based on the ideXlab platform.
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simulations of changes to glaciar zongo bolivia 16 s over the 21st century using a 3 d full Stokes Model and cmip5 climate projections
Annals of Glaciology, 2015Co-Authors: Marion Reveillet, Antoine Rabatel, Fabien Gilletchaulet, Alvaro SorucoAbstract:Bolivian glaciers are an essential source of fresh water for the Altiplano, and any changes they may undergo in the near future due to ongoing climate change are of particular concern. Glaciar Zongo, Bolivia, located near the administrative capital La Paz, has been extensively monitored by the GLACIOCLIM observatory in the last two decades. Here we Model the glacier dynamics using the 3-D full-Stokes Model Elmer/Ice. The Model was calibrated and validated over a recent period (1997–2010) using four independent datasets: available observations of surface velocities and surface mass balance were used for calibration, and changes in surface elevation and retreat of the glacier front were used for validation. Over the validation period, Model outputs are in good agreement with observations (differences less than a small percentage). The future surface mass balance is assumed to depend on the equilibrium-line altitude (ELA) and temperature changes through the sensitivity of ELA to temperature. The Model was then forced for the 21st century using temperature changes projected by nine Coupled Model Intercomparison Project phase 5 (CMIP5) Models. Here we give results for three different representative concentration pathways (RCPs). The intermediate scenario RCP6.0 led to 69�7% volume loss by 2100, while the two extreme scenarios, RCP2.6 and RCP8.5, led to 40�7% and 89� 4% loss of volume, respectively.
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Simulations of changes to Glaciar Zongo, Bolivia (16°S), over the 21st century using a 3-D full-Stokes Model and CMIP5 climate projections
Annals of Glaciology, 2015Co-Authors: Marion Reveillet, Fabien Gillet-chaulet, Antoine Rabatel, Alvaro SorucoAbstract:Bolivian glaciers are an essential source of fresh water for the Altiplano, and any changes they may undergo in the near future due to ongoing climate change are of particular concern. Glaciar Zongo, Bolivia, located near the administrative capital La Paz, has been extensively monitored by the GLACIOCLIM observatory in the last two decades. Here we Model the glacier dynamics using the 3-D full-Stokes Model Elmer/Ice. The Model was calibrated and validated over a recent period (1997–2010) using four independent datasets: available observations of surface velocities and surface mass balance were used for calibration, and changes in surface elevation and retreat of the glacier front were used for validation. Over the validation period, Model outputs are in good agreement with observations (differences less than a small percentage). The future surface mass balance is assumed to depend on the equilibrium-line altitude (ELA) and temperature changes through the sensitivity of ELA to temperature. The Model was then forced for the 21st century using temperature changes projected by nine Coupled Model Intercomparison Project phase 5 (CMIP5) Models. Here we give results for three different representative concentration pathways (RCPs). The intermediate scenario RCP6.0 led to 69�7% volume loss by 2100, while the two extreme scenarios, RCP2.6 and RCP8.5, led to 40�7% and 89� 4% loss of volume, respectively.
Huanyao Wen - One of the best experts on this subject based on the ideXlab platform.
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Weak solutions of a two-phase Navier–Stokes Model with a general slip law
Journal of Functional Analysis, 2015Co-Authors: Steinar Evje, Huanyao WenAbstract:Abstract This work is devoted to a study of a gas–liquid Navier–Stokes Model with a general slip law that allows the two phases to flow with unequal fluid velocity. The slip law is general enough to describe counter-current flow, i.e., a situation where gas and liquid move in opposite direction. Motivated by applications in the context of wellbore flow systems we assume that there is a free interface which separates the gas–liquid mixture region from a strongly gas dominated region which holds a specified positive pressure p ⁎ . The slip law is incorporated in the mass and momentum equations resulting in a Model where flow is described in terms of the gas velocity. However, the mixture momentum equation contains a generalized pressure law composed of the standard pressure function combined with three new terms that depend on parameters characterizing the difference between gas and liquid velocity. These new terms make the analysis challenging. By carefully exploiting the positive external pressure p ⁎ we are able to obtain uniform lower and upper bounds on a pressure-related quantity. This in turn allows for various higher order regularity estimates which imply that global existence and uniqueness of weak solutions can be shown.