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Modelling of convective phenomena in forest fire.

M.ª Isabel Asensio, Luis Ferragut, Jacques Simon (2002)

RACSAM

We present a model coupling the fire propagation equations in a bidimensional domain representing the surface, and the air movement equations in a three dimensional domain representing an air layer. As the air layer thickness is small compared with its length, an asymptotic analysis gives a three dimensional convective model governed by a bidimensional equation verified by a stream function. We also present the numerical simulations of these equations.

Modelling of miscible liquids with the Korteweg stress

Ilya Kostin, Martine Marion, Rozenn Texier-Picard, Vitaly A. Volpert (2003)

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

When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove the global existence...

Modelling of Miscible Liquids with the Korteweg Stress

Ilya Kostin, Martine Marion, Rozenn Texier-Picard, Vitaly A. Volpert (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove the global...

More pressure in the finite element discretization of the Stokes problem

Christine Bernardi, Frédéric Hecht (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

For the Stokes problem in a two- or three-dimensional bounded domain, we propose a new mixed finite element discretization which relies on a nonconforming approximation of the velocity and a more accurate approximation of the pressure. We prove that the velocity and pressure discrete spaces are compatible, in the sense that they satisfy an inf-sup condition of Babuška and Brezzi type, and we derive some error estimates.

Mortar finite element discretization of a model coupling Darcy and Stokes equations

Christine Bernardi, Tomás Chacón Rebollo, Frédéric Hecht, Zoubida Mghazli (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

As a first draft of a model for a river flowing on a homogeneous porous ground, we consider a system where the Darcy and Stokes equations are coupled via appropriate matching conditions on the interface. We propose a discretization of this problem which combines the mortar method with standard finite elements, in order to handle separately the flow inside and outside the porous medium. We prove a priori and a posteriori error estimates for the resulting discrete problem. Some numerical experiments...

Multimodels for incompressible flows : iterative solutions for the Navier-Stokes / Oseen coupling

L. Fatone, P. Gervasio, A. Quarteroni (2001)

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

In a recent paper [4] we have proposed and analysed a suitable mathematical model which describes the coupling of the Navier-Stokes with the Oseen equations. In this paper we propose a numerical solution of the coupled problem by subdomain splitting. After a preliminary analysis, we prove a convergence result for an iterative algorithm that alternates the solution of the Navier-Stokes problem to the one of the Oseen problem.

Multimodels for incompressible flows: iterative solutions for the Navier-Stokes/Oseen coupling

L. Fatone, P. Gervasio, A. Quarteroni (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In a recent paper [4] we have proposed and analysed a suitable mathematical model which describes the coupling of the Navier-Stokes with the Oseen equations. In this paper we propose a numerical solution of the coupled problem by subdomain splitting. After a preliminary analysis, we prove a convergence result for an iterative algorithm that alternates the solution of the Navier-Stokes problem to the one of the Oseen problem.

Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem

Aihui Zhou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, a multi-parameter error resolution technique is applied into a mixed finite element method for the Stokes problem. By using this technique and establishing a multi-parameter asymptotic error expansion for the mixed finite element method, an approximation of higher accuracy is obtained by multi-processor computers in parallel.

Navier-Stokes equations on unbounded domains with rough initial data

Peer Christian Kunstmann (2010)

Czechoslovak Mathematical Journal

We consider the Navier-Stokes equations in unbounded domains Ω ⊆ ℝ n of uniform C 1 , 1 -type. We construct mild solutions for initial values in certain extrapolation spaces associated to the Stokes operator on these domains. Here we rely on recent results due to Farwig, Kozono and Sohr, the fact that the Stokes operator has a bounded H ∞ -calculus on such domains, and use a general form of Kato’s method. We also obtain information on the corresponding pressure term.

Currently displaying 501 – 520 of 1082