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On a diphasic low Mach number system

Stéphane Dellacherie (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose a Diphasic Low Mach Number (DLMN) system for the modelling of diphasic flows without phase change at low Mach number, system which is an extension of the system proposed by Majda in [Center of Pure and Applied Mathematics, Berkeley, report No. 112] and [Combust. Sci. Tech. 42 (1985) 185–205] for low Mach number combustion problems. This system is written for a priori any equations of state. Under minimal thermodynamic hypothesis which are satisfied by a large class of generalized van...

On a diphasic low mach number system

Stéphane Dellacherie (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a Diphasic Low Mach Number (DLMN) system for the modelling of diphasic flows without phase change at low Mach number, system which is an extension of the system proposed by Majda in [Center of Pure and Applied Mathematics, Berkeley, report No. 112] and [Combust. Sci. Tech.42 (1985) 185–205] for low Mach number combustion problems. This system is written for a priori any equations of state. Under minimal thermodynamic hypothesis which are satisfied by a large class of generalized van...

On a hybrid finite-volume-particle method

Alina Chertock, Alexander Kurganov (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the one- and two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)], where the one-dimensional finite-volume-particle method has been proposed. The core idea behind the...

On a hybrid finite-volume-particle method

Alina Chertock, Alexander Kurganov (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the one- and two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)], where the one-dimensional finite-volume-particle method has been proposed. The core idea behind the...

On a method for a-posteriori error estimation of approximate solutions to parabolic problems

Juraj Weisz (1994)

Commentationes Mathematicae Universitatis Carolinae

The aim of the paper is to derive a method for the construction of a-posteriori error estimate to approximate solutions to parabolic initial-boundary value problems. The computation of the suggested error bound requires only the computation of a finite number of systems or linear algebraic equations. These systems can be solved parallelly. It is proved that the suggested a-posteriori error estimate tends to zero if the approximation tends to the true solution.

On a nonlinear stationary problem in unbounded domains.

Carlos Frederico Vasconcellos (1992)

Revista Matemática de la Universidad Complutense de Madrid

We study existence and some properties of solutions of the nonlinear elliptic equation N(x,a(u))Lu = f in unbounded domains. The above method is not a variational problem. Our techniques involve fixed point arguments and Galerkin method.

On a parabolic problem with nonlinear Newton boundary conditions

Miloslav Feistauer, Karel Najzar, Karel Švadlenka (2002)

Commentationes Mathematicae Universitatis Carolinae

The paper is concerned with the study of a parabolic initial-boundary value problem with nonlinear Newton boundary condition considered in a two-dimensional domain. The goal is to prove the existence and uniqueness of a weak solution to the problem in the case when the nonlinearity in the Newton boundary condition does not satisfy any monotonicity condition and to analyze the finite element approximation.

On a Parallel Implementation of the Mortar Element Method

Gassav S. Abdoulaev, Yves Achdou, Yuri A. Kuznetsov, Christophe Prud'homme (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We discuss a parallel implementation of the domain decomposition method based on the macro-hybrid formulation of a second order elliptic equation and on an approximation by the mortar element method. The discretization leads to an algebraic saddle- point problem. An iterative method with a block- diagonal preconditioner is used for solving the saddle- point problem. A parallel implementation of the method is emphasized. Finally the results of numerical experiments are presented.

On adaptive BDDC for the flow in heterogeneous porous media

Bedřich Sousedík (2019)

Applications of Mathematics

We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for numerical solution of a single-phase flow in heterogeneous porous media. The method solves for both flux and pressure variables. The fluxes are resolved in three steps: the coarse solve is followed by subdomain solves and last we look for a divergence-free flux correction and pressures using conjugate gradients with the BDDC preconditioner. Our main contribution is an application of the adaptive algorithm for selection...

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