In the present paper, we investigate several cubic equations of state widely used in the literature, for which we are able to construct analytically the complete law. In order to describe two-phase flows, we use Maxwell's construction, which amounts to consider pure phases and a mixture zone at saturation. The parameters appearing in the different equations of state are fitted in order to be precise in the saturation zone at high pressures. The different laws are then compared in a large range of pressures, showing the best accuracy of Clausius equation of state.
{"title":"Comparison of several complete cubic laws for two-phase flow models","authors":"Gloria Faccanoni, Bérénice Grec","doi":"10.1051/proc/202372117","DOIUrl":"https://doi.org/10.1051/proc/202372117","url":null,"abstract":"In the present paper, we investigate several cubic equations of state widely used in the literature, for which we are able to construct analytically the complete law. In order to describe two-phase flows, we use Maxwell's construction, which amounts to consider pure phases and a mixture zone at saturation. The parameters appearing in the different equations of state are fitted in order to be precise in the saturation zone at high pressures. The different laws are then compared in a large range of pressures, showing the best accuracy of Clausius equation of state.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80141074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
L. Chaintron, Álvaro Mateos González, L. Mertz, Philippe Moireau
We address the problem of deterministic sequential estimation for a nonsmooth dynamics governed by a variational inequality. An example of such dynamics is the Skorokhod problem with a reflective boundary condition. For smooth dynamics, Mortensen introduced in 1968 a nonlinear estimator based on likelihood maximisation. Then, starting with Hijab in 1980, several authors established a connection between Mortensen’s approach and the vanishing noise limit of the robust form of the so-called Zakai equation. In this paper, we investigate to what extent these methods can be developed for dynamics governed by a variational inequality. On the one hand, we address this problem by relaxing the inequality constraint by penalization: this yields an approximate Mortensen estimator relying on an approximating smooth dynamics. We verify that the equivalence between the deterministic and stochastic approaches holds through a vanishing noise limit. On the other hand, inspired by the smooth dynamics approach, we study the vanishing viscosity limit of the Hamilton-Jacobi equation satisfied by the Hopf-Cole transform of the solution of the robust Zakai equation. In contrast to the case of smooth dynamics, the zero-noise limit of the robust form of the Zakai equation cannot be understood in our case from the Bellman equation on the value function arising in Mortensen’s procedure. This unveils a violation of equivalence for dynamics governed by a variational inequality between the Mortensen approach and the low noise stochastic approach for nonsmooth dynamics.
{"title":"Mortensen observer for a class of variational inequalities – lost equivalence with stochastic filtering approaches","authors":"L. Chaintron, Álvaro Mateos González, L. Mertz, Philippe Moireau","doi":"10.1051/proc/202373130","DOIUrl":"https://doi.org/10.1051/proc/202373130","url":null,"abstract":"We address the problem of deterministic sequential estimation for a nonsmooth dynamics governed by a variational inequality. An example of such dynamics is the Skorokhod problem with a reflective boundary condition. For smooth dynamics, Mortensen introduced in 1968 a nonlinear estimator based on likelihood maximisation. Then, starting with Hijab in 1980, several authors established a connection between Mortensen’s approach and the vanishing noise limit of the robust form of the so-called Zakai equation. In this paper, we investigate to what extent these methods can be developed for dynamics governed by a variational inequality. On the one hand, we address this problem by relaxing the inequality constraint by penalization: this yields an approximate Mortensen estimator relying on an approximating smooth dynamics. We verify that the equivalence between the deterministic and stochastic approaches holds through a vanishing noise limit. On the other hand, inspired by the smooth dynamics approach, we study the vanishing viscosity limit of the Hamilton-Jacobi equation satisfied by the Hopf-Cole transform of the solution of the robust Zakai equation. In contrast to the case of smooth dynamics, the zero-noise limit of the robust form of the Zakai equation cannot be understood in our case from the Bellman equation on the value function arising in Mortensen’s procedure. This unveils a violation of equivalence for dynamics governed by a variational inequality between the Mortensen approach and the low noise stochastic approach for nonsmooth dynamics.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78543213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hamza Boukraichi, N. Razaaly, N. Akkari, F. Casenave, D. Ryckelynck
In the following work, a benchmark of different non-intrusive model reduction approaches is performed on an explicit dynamic contact 3D-problem. The main purpose of this work is to evaluate the stability of the reduced model with respect to time along with the precision of these approaches with respect to the true solutions of interest. These solutions are the prediction of displacement and velocity fields. The precision of these approaches is also evaluated with respect to the evolution of some materials parameters. Six parameters vary in this study and we would like to predict the whole transient fast dynamic impact response with respect to each parameters. To this end, several models are trained : Proper Orthogonal Decomposition (POD) and Deep convolutional Neural Network (DcNN), in addition, a vectorized version of Interpolation in Grassman Manifolds is proposed. The benchmark performed illustrate that using DcNN’s allows to achieve the best precision and stability in predicting physical fields.
{"title":"Parametrized non intrusive space-time approximation for explicit dynamic fem applications","authors":"Hamza Boukraichi, N. Razaaly, N. Akkari, F. Casenave, D. Ryckelynck","doi":"10.1051/proc/202373068","DOIUrl":"https://doi.org/10.1051/proc/202373068","url":null,"abstract":"In the following work, a benchmark of different non-intrusive model reduction approaches is performed on an explicit dynamic contact 3D-problem. The main purpose of this work is to evaluate the stability of the reduced model with respect to time along with the precision of these approaches with respect to the true solutions of interest. These solutions are the prediction of displacement and velocity fields. The precision of these approaches is also evaluated with respect to the evolution of some materials parameters. Six parameters vary in this study and we would like to predict the whole transient fast dynamic impact response with respect to each parameters. To this end, several models are trained : Proper Orthogonal Decomposition (POD) and Deep convolutional Neural Network (DcNN), in addition, a vectorized version of Interpolation in Grassman Manifolds is proposed. The benchmark performed illustrate that using DcNN’s allows to achieve the best precision and stability in predicting physical fields.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86718582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work is motivated by the modelling a liquid-vapour flows with phase transition describing the evolution of the coolant within an heat exchanger (e.g. the core of a Pressurized Water Reactor). We investigate an advection-diffusion equation with a degenerate and nonlinear diffusion coefficient. The degeneracy corresponds to a liquid-vapor mixture in the original model whereas the diffusion coefficient is non-degenerate in the pure phase cases. We focus on the influence of the diffusion coefficient on a simple 1D configuration for which some analytical computations can be done, leading to a surprising behavior of the phase transition with respect to the diffusion.
{"title":"Influence of a nonlinear degenerate diffusion on an advection-diffusion equation in a diffuse interface framework","authors":"Gloria Faccanoni, C. Galusinski","doi":"10.1051/proc/202372143","DOIUrl":"https://doi.org/10.1051/proc/202372143","url":null,"abstract":"This work is motivated by the modelling a liquid-vapour flows with phase transition describing the evolution of the coolant within an heat exchanger (e.g. the core of a Pressurized Water Reactor). We investigate an advection-diffusion equation with a degenerate and nonlinear diffusion coefficient. The degeneracy corresponds to a liquid-vapor mixture in the original model whereas the diffusion coefficient is non-degenerate in the pure phase cases. We focus on the influence of the diffusion coefficient on a simple 1D configuration for which some analytical computations can be done, leading to a surprising behavior of the phase transition with respect to the diffusion.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85917578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. Alizadeh, Sara Costa Faya, Haibo Liu, D. Lombardi, Sylvain Bernasconi, P. Guns, M. Markert
The aim of this work is to provide a preliminary comparison of different classes of methods to automatically detect the effect of ageing from in vivo data. The application which motivated this work is related to safety pharmacology, whose major goal is to determine, in a pre-clinical phase, whether a drug is potentially dangerous for the health. In particular, we are going to compare statistical, machine learning and mathematical modelling methods.
{"title":"Comparison of statistical, machine learning, and mathematical modelling methods to investigate the effect of ageing on dog’s cardiovascular system","authors":"E. Alizadeh, Sara Costa Faya, Haibo Liu, D. Lombardi, Sylvain Bernasconi, P. Guns, M. Markert","doi":"10.1051/proc/202373002","DOIUrl":"https://doi.org/10.1051/proc/202373002","url":null,"abstract":"The aim of this work is to provide a preliminary comparison of different classes of methods to automatically detect the effect of ageing from in vivo data. The application which motivated this work is related to safety pharmacology, whose major goal is to determine, in a pre-clinical phase, whether a drug is potentially dangerous for the health. In particular, we are going to compare statistical, machine learning and mathematical modelling methods.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78900660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work concerns the analysis of the relaxation processes toward thermodynamical equilibrium arising in a compressible immiscible two-phase flow. Classically the relaxation processes are taken into account through dynamical systems which are coupled to the dynamics of the flow. The present paper compares two types of source terms which are commonly used: a BGK-like system and a mixture entropy gradient type. For both systems, main properties are investigated (agreement with second principle of thermodynamics, existence of solutions, maximum principle,...) and numerical experiments illustrate their asymptotic behaviour.
{"title":"Study of relaxation processes in a two-phase flow model","authors":"J. Bussac","doi":"10.1051/proc/202372002","DOIUrl":"https://doi.org/10.1051/proc/202372002","url":null,"abstract":"This work concerns the analysis of the relaxation processes toward thermodynamical equilibrium arising in a compressible immiscible two-phase flow. Classically the relaxation processes are taken into account through dynamical systems which are coupled to the dynamics of the flow. The present paper compares two types of source terms which are commonly used: a BGK-like system and a mixture entropy gradient type. For both systems, main properties are investigated (agreement with second principle of thermodynamics, existence of solutions, maximum principle,...) and numerical experiments illustrate their asymptotic behaviour.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74400414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. Frioux, S. Huet, S. Labarthe, Julien Martinelli, T. Malou, David Sherman, Marie-Luce Taupin, Pablo Ugalde-Salas
Mathematical and numerical models are increasingly used in microbial ecology to model the fate of microbial communities in their ecosystem. These models allow to connect in a mechanistic framework species-level informations, such as the microbial genomes, with macro-scale features, such as species spatial distributions or metabolite gradients. Numerous models are built upon species-level metabolic models that predict the metabolic behaviour of a microbe by solving an optimization problem knowing its genome and its nutritional environment. However, screening the community dynamics with these metabolic models implies to solve such an optimization problem by species at each time step, leading to a significant computational load further increased by several orders of magnitude when spatial dimensions are added. In this paper, we propose a statistical framework based on Reproducing Kernel Hilbert Space (RKHS) metamodels that are used to provide fast approximations of the original metabolic model. The metamodel can replace the optimization step in the system dynamics, providing comparable outputs at a much lower computational cost. We will first build a system dynamics model of a simplified gut microbiota composed of a unique commensal bacterial strain in interaction with the host and challenged by a Salmonella infection. Then, the machine learning method will be introduced, and particularly the ANOVA-RKHS that will be exploited to achieve variable selection and model parsimony. A training dataset will be constructed with the original system dynamics model and hyper-parameters will be carefully chosen to provide fast and accurate approximations of the original model. Finally, the accuracy of the trained metamodels will be assessed, in particular by comparing the system dynamics outputs when the original model is replaced by its metamodel. The metamodel allows an overall relative error of 4.71% but reducing the computational load by a speed-up factor higher than 45, while correctly reproducing the complex behaviour occurring during Salmonella infection. These results provide a proof-of-concept of the potentiality of machine learning methods to give fast approximations of metabolic model outputs and pave the way towards PDE-based spatio-temporal models of microbial communities including microbial metabolism and host-microbiota-pathogen interactions.
{"title":"Accelerating metabolic models evaluation with statistical metamodels: application to Salmonella infection models","authors":"C. Frioux, S. Huet, S. Labarthe, Julien Martinelli, T. Malou, David Sherman, Marie-Luce Taupin, Pablo Ugalde-Salas","doi":"10.1051/proc/202373187","DOIUrl":"https://doi.org/10.1051/proc/202373187","url":null,"abstract":"Mathematical and numerical models are increasingly used in microbial ecology to model the fate of microbial communities in their ecosystem. These models allow to connect in a mechanistic framework species-level informations, such as the microbial genomes, with macro-scale features, such as species spatial distributions or metabolite gradients. Numerous models are built upon species-level metabolic models that predict the metabolic behaviour of a microbe by solving an optimization problem knowing its genome and its nutritional environment. However, screening the community dynamics with these metabolic models implies to solve such an optimization problem by species at each time step, leading to a significant computational load further increased by several orders of magnitude when spatial dimensions are added. In this paper, we propose a statistical framework based on Reproducing Kernel Hilbert Space (RKHS) metamodels that are used to provide fast approximations of the original metabolic model. The metamodel can replace the optimization step in the system dynamics, providing comparable outputs at a much lower computational cost. We will first build a system dynamics model of a simplified gut microbiota composed of a unique commensal bacterial strain in interaction with the host and challenged by a Salmonella infection. Then, the machine learning method will be introduced, and particularly the ANOVA-RKHS that will be exploited to achieve variable selection and model parsimony. A training dataset will be constructed with the original system dynamics model and hyper-parameters will be carefully chosen to provide fast and accurate approximations of the original model. Finally, the accuracy of the trained metamodels will be assessed, in particular by comparing the system dynamics outputs when the original model is replaced by its metamodel. The metamodel allows an overall relative error of 4.71% but reducing the computational load by a speed-up factor higher than 45, while correctly reproducing the complex behaviour occurring during Salmonella infection. These results provide a proof-of-concept of the potentiality of machine learning methods to give fast approximations of metabolic model outputs and pave the way towards PDE-based spatio-temporal models of microbial communities including microbial metabolism and host-microbiota-pathogen interactions.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77509792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
V. Ehrlacher, D. Lombardi, O. Mula, Fabio Nobile, Tommaso Taddei
This special volume gathers research works that have been conducted during the 25th edition of the summer school CEMRACS (Centre d’´Et´e Math´ematique de Recherche Avanc´ee en Calcul Scientifique), which took place at CIRM (Centre International de Rencontre Math´ematique) in Luminy from July 19th to August 27th, 2021. CEMRACS is an event initiated in 1996 by Yvon Maday and Fr´ed´eric Coquel. It takes place every year at CIRM in Luminy (Marseille, France) for six weeks. The aim is to bring together scientists from both the academic and industrial communities to exchange ideas about a modern and relevant scientific topic which is selected by the CIRM scientific committee. CEMRACS is composed of two parts. The first is a one-week summer school with lectures of leading scientists where the goal is to give an overview of the topic to non-expert participants. The remaining five weeks are dedicated to research projects proposed by academic scientists or industrial partners. Each project is carried out by a small group of students under the supervision of experienced researchers. Experience from the previous years has shown the significant positive impact of the CEMRACS, not only on the development of these short-term projects, but also on the interactions between mathematics, applied sciences and industry. The event of 2021 focused on ”Data Assimilation and Reduced Modeling for High Dimensional Problems”. A significant challenge arising in increasingly many modern applications is how to blend complex mathematical models, often based on differential or integral equations, with the large and, possibly, noisy data sets which are now routinely available in many fields of engineering, science and technology. Growing efforts are made to develop a coherent mathematical framework where one of the main obstructions is the high dimensionality of the involved mathematical objects, which requires efficient sampling or optimization techniques for large-scale problems and, possibly, model order reduction strategies. The CEMRACS 2021 was devoted to this topic of data assimilation and model reduction in high-dimensional problems. It is by nature interdisciplinary, not only by the amount of the different mathematical skills that need to be invoked, but also by the detailed knowledge that
这本特别的书收集了第25届暑期学校CEMRACS (Centre d ' ' Et ' e Math ' ematique de Recherche Avanc ' ee en Calcul Scientifique)期间进行的研究工作，该暑期学校于2021年7月19日至8月27日在Luminy的CIRM (Centre International de Rencontre Math ' ematique)举行。CEMRACS是由Yvon Maday和eric Coquel于1996年发起的一项活动。它每年在法国马赛卢明的CIRM举行，为期六周。其目的是汇集来自学术界和工业界的科学家，就由CIRM科学委员会选择的现代和相关的科学主题交换意见。CEMRACS由两部分组成。第一个是为期一周的暑期学校，由顶尖科学家讲课，目的是向非专业参与者提供该主题的概述。剩下的五周是专门用于学术科学家或工业合作伙伴提出的研究项目。每个项目都由一小组学生在经验丰富的研究人员的监督下进行。前几年的经验表明，CEMRACS不仅对这些短期项目的发展，而且对数学、应用科学和工业之间的相互作用产生了重大的积极影响。2021年的主题是“高维问题的数据同化和简化建模”。在越来越多的现代应用中出现的一个重大挑战是如何将复杂的数学模型(通常基于微分或积分方程)与现在在许多工程、科学和技术领域中常规可用的大型且可能有噪声的数据集混合在一起。越来越多的人努力开发一个连贯的数学框架，其中一个主要障碍是所涉及的数学对象的高维性，这需要有效的采样或优化技术来解决大规模问题，可能还需要模型降阶策略。CEMRACS 2021致力于高维问题中的数据同化和模型缩减这一主题。从本质上讲，它是跨学科的，不仅需要调用不同的数学技能，而且还需要详细的知识
{"title":"Editorial of CEMRACS 2021","authors":"V. Ehrlacher, D. Lombardi, O. Mula, Fabio Nobile, Tommaso Taddei","doi":"10.1051/proc/202373001","DOIUrl":"https://doi.org/10.1051/proc/202373001","url":null,"abstract":"This special volume gathers research works that have been conducted during the 25th edition of the summer school CEMRACS (Centre d’´Et´e Math´ematique de Recherche Avanc´ee en Calcul Scientifique), which took place at CIRM (Centre International de Rencontre Math´ematique) in Luminy from July 19th to August 27th, 2021. CEMRACS is an event initiated in 1996 by Yvon Maday and Fr´ed´eric Coquel. It takes place every year at CIRM in Luminy (Marseille, France) for six weeks. The aim is to bring together scientists from both the academic and industrial communities to exchange ideas about a modern and relevant scientific topic which is selected by the CIRM scientific committee. CEMRACS is composed of two parts. The first is a one-week summer school with lectures of leading scientists where the goal is to give an overview of the topic to non-expert participants. The remaining five weeks are dedicated to research projects proposed by academic scientists or industrial partners. Each project is carried out by a small group of students under the supervision of experienced researchers. Experience from the previous years has shown the significant positive impact of the CEMRACS, not only on the development of these short-term projects, but also on the interactions between mathematics, applied sciences and industry. The event of 2021 focused on ”Data Assimilation and Reduced Modeling for High Dimensional Problems”. A significant challenge arising in increasingly many modern applications is how to blend complex mathematical models, often based on differential or integral equations, with the large and, possibly, noisy data sets which are now routinely available in many fields of engineering, science and technology. Growing efforts are made to develop a coherent mathematical framework where one of the main obstructions is the high dimensionality of the involved mathematical objects, which requires efficient sampling or optimization techniques for large-scale problems and, possibly, model order reduction strategies. The CEMRACS 2021 was devoted to this topic of data assimilation and model reduction in high-dimensional problems. It is by nature interdisciplinary, not only by the amount of the different mathematical skills that need to be invoked, but also by the detailed knowledge that","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80230181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Katia Ait-Ameur, S. Kokh, M. Massot, M. Pelanti, T. Pichard
This work focuses on the numerical approximation of the barotropic Baer-Nunziato two-phase flow model. We propose a numerical scheme that relies on an operator splitting method corresponding to a separate treatment of the acoustic and the material transport phenomena. In the subsonic case, this also corresponds to a separate treatment of the fast and the slow propagation phenomena. This approach follows the lines of the implicit-explicit schemes developed in [8]. The operator splitting enable the use of time steps that are no longer constrained by the sound velocity thanks to an implicit treatment of the acoustic waves, while maintaining accuracy in the subsonic regime thanks to an explicit treatment of the material waves. In the present setting, a particular attention will be also given to the discretization of the non-conservative terms that figure in the two-phase model. We prove that the proposed numerical strategy is positivity preserving for the volume fractions and the partial masses. The scheme is tested against several one-dimensional test cases including flows featuring vanishing phases.
{"title":"An acoustic-transport splitting method for the barotropic Baer-Nunziato two-phase flow model","authors":"Katia Ait-Ameur, S. Kokh, M. Massot, M. Pelanti, T. Pichard","doi":"10.1051/proc/202372093","DOIUrl":"https://doi.org/10.1051/proc/202372093","url":null,"abstract":"This work focuses on the numerical approximation of the barotropic Baer-Nunziato two-phase flow model. We propose a numerical scheme that relies on an operator splitting method corresponding to a separate treatment of the acoustic and the material transport phenomena. In the subsonic case, this also corresponds to a separate treatment of the fast and the slow propagation phenomena. This approach follows the lines of the implicit-explicit schemes developed in [8]. The operator splitting enable the use of time steps that are no longer constrained by the sound velocity thanks to an implicit treatment of the acoustic waves, while maintaining accuracy in the subsonic regime thanks to an explicit treatment of the material waves. In the present setting, a particular attention will be also given to the discretization of the non-conservative terms that figure in the two-phase model. We prove that the proposed numerical strategy is positivity preserving for the volume fractions and the partial masses. The scheme is tested against several one-dimensional test cases including flows featuring vanishing phases.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79217598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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