7 research outputs found
Coupling 3D Navier-Stokes and 1D shallow water models
International audienceThe present work addresses the problem of coupling hydrodynamical models with different spatial dimensions, which can be used in order to reduce the computational cost of river numerical models. We show that this problem can be tackled quite efficiently by designing a simple algorithm using techniques borrowed from domain decomposition theory. This algorithm is non intrusive, i.e. allows using existing numerical models with very few modifications. The method is illustrated on an academic test-case, namely a free surface flow in a bend-shaped channel. A 3-D Navier-Stokes model is coupled with a 1-D shallow water model, and results are compared to those obtained in a fully 3-D case. It is shown that the coupling algorithm provides an accurate solution, which can be improved thanks to an iterative algorithm (Schwarz method). This study is performed using the Mascaret-Telemac system
Coupling 3D Navier-Stokes and 1D shallow water models
International audienceThe present work addresses the problem of coupling hydrodynamical models with different spatial dimensions, which can be used in order to reduce the computational cost of river numerical models. We show that this problem can be tackled quite efficiently by designing a simple algorithm using techniques borrowed from domain decomposition theory. This algorithm is non intrusive, i.e. allows using existing numerical models with very few modifications. The method is illustrated on an academic test-case, namely a free surface flow in a bend-shaped channel. A 3-D Navier-Stokes model is coupled with a 1-D shallow water model, and results are compared to those obtained in a fully 3-D case. It is shown that the coupling algorithm provides an accurate solution, which can be improved thanks to an iterative algorithm (Schwarz method). This study is performed using the Mascaret-Telemac system
Design of a Schwarz coupling method for a dimensionally heterogeneous problem
International audienceWhen dealing with simulation of complex physical phenomena, one may have to couple several models which levels of complexity and computational cost are adapted to the local behavior of the system. In order to avoid heavy numerical simulations, one can use the most complex model only at locations where the physics makes it necessary, and the simplest ones - usually obtained after simpli cations - everywhere else. Such simpli cations in the models may involve a change in the geometry and the dimension of the physical domain. In that case, one deals with dimensionally heterogeneous coupling. Such a coupling has already been applied in several applications related to the study of human blood system and in the context of river dynamics. Our final objective is to derive an effi cient coupling strategy between 1-D/2-D shallow water equations and 2-D/3-D Navier-Stokes system. As a fi rst step in this direction and in order to identify the main questions that we will have to face, we will present in this talk a preliminary study in which we couple a 2-D Laplace equation with non symmetric boundary conditions with a corresponding 1-D Laplace equation. We will fi rst show how to obtain the 1-D model from the 2-D one by integration along one direction, by analogy with the link between shallow water equations and the Navier-Stokes system. Then, we will focus on the design of an e cient Schwarz-like iterative coupling method. We will discuss the choice of boundary conditions at coupling interfaces. We will prove the convergence of such algorithms and give some theoretical results related to the choice of the location of the coupling interface, and the control of the error between a global 2-D reference solution and the 2-D coupled one. These theoretical results will be illustrated numerically. This work is performed in the context of a collaboration with EDF R&D
Boundary conditions and Schwarz waveform relaxation method for linear viscous Shallow Water equations in hydrodynamics
International audienceWe propose in the present work an extension of the Schwarz waveform relaxation method to the case of viscous shallow water system with advection term. We first show the difficulties that arise when approximating the Dirichlet to Neumann operators if we consider an asymptotic analysis based on large Reynolds number regime and a small domain aspect ratio. Therefore we focus on the design of a Schwarz algorithm with Robin like boundary conditions. We prove the well-posedness and the convergence of the algorithm
Design of a Schwarz coupling method for a dimensionally heterogeneous problem
International audienceWhen dealing with simulation of complex physical phenomena, one may have to couple several models which levels of complexity and computational cost are adapted to the local behavior of the system. In order to avoid heavy numerical simulations, one can use the most complex model only at locations where the physics makes it necessary, and the simplest ones - usually obtained after simpli cations - everywhere else. Such simpli cations in the models may involve a change in the geometry and the dimension of the physical domain. In that case, one deals with dimensionally heterogeneous coupling. Such a coupling has already been applied in several applications related to the study of human blood system and in the context of river dynamics. Our final objective is to derive an effi cient coupling strategy between 1-D/2-D shallow water equations and 2-D/3-D Navier-Stokes system. As a fi rst step in this direction and in order to identify the main questions that we will have to face, we will present in this talk a preliminary study in which we couple a 2-D Laplace equation with non symmetric boundary conditions with a corresponding 1-D Laplace equation. We will fi rst show how to obtain the 1-D model from the 2-D one by integration along one direction, by analogy with the link between shallow water equations and the Navier-Stokes system. Then, we will focus on the design of an e cient Schwarz-like iterative coupling method. We will discuss the choice of boundary conditions at coupling interfaces. We will prove the convergence of such algorithms and give some theoretical results related to the choice of the location of the coupling interface, and the control of the error between a global 2-D reference solution and the 2-D coupled one. These theoretical results will be illustrated numerically. This work is performed in the context of a collaboration with EDF R&D
Design and analysis of a Schwarz coupling method for a dimensionally heterogeneous problem
International audienceIn the present work, we study and analyze an efficient iterative coupling method for a dimensionally heterogeneous problem . We consider the case of 2-D Laplace equation with non symmetric boundary conditions with a corresponding 1-D Laplace equation. We will first show how to obtain the 1-D model from the 2-D one by integration along one direction, by analogy with the link between shallow water equations and the Navier-Stokes system. Then, we will focus on the design of an Schwarz-like iterative coupling method. We will discuss the choice of boundary conditions at coupling interfaces. We will prove the convergence of such algorithms and give some theoretical results related to the choice of the location of the coupling interface, and the control of the difference between a global 2-D reference solution and the 2-D coupled one. These theoretical results will be illustrated numerically.Dans ce document nous étudions et analysons et une méthode de couplage multidimensionnel itérative. Nous considérons le cas de l'équation de Laplace 2-D avec des conditions aux bords non symétriques, couplée avec une équation de Laplace 1-D correspondante. dans un premier temps nous montrons comment obtenir le modèle 1-D à partir du modèle 2-D par intégration verticale et par analogie avec la dérivation des équations de Saint-Venant à partir des équations de Navier-Stokes. Ensuite nous présentons un algorithme de couplage de type Schwarz. Nous discutons le choix des conditions aux interfaces de couplage. Nous démontrons la convergence de tels algorithmes et donnons quelques résultats théoriques sur le choix de la position des interfaces de couplage. Un résultat théorique sur le contrôle de l'erreur entre la solution globale 2-D de référence et la solution 2-D couplée sera aussi donné. Enfin nous illustrons ces résultats numériquement