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Some special solutions of self similar type in MHD, obtained by a separation method of variables

Michel Cessenat, Philippe Genta (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We use a method based on a separation of variables for solving a first order partial differential equations system, using a very simple modelling of MHD. The method consists in introducing three unknown variables Φ1, Φ2, Φ3 in addition to the time variable t and then in searching a solution which is separated with respect to Φ1 and t only. This is allowed by a very simple relation, called a “metric separation equation”, which governs the type of solutions with respect to time. The families...

Space-time variational saddle point formulations of Stokes and Navier–Stokes equations

Rafaela Guberovic, Christoph Schwab, Rob Stevenson (2014)

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

The instationary Stokes and Navier−Stokes equations are considered in a simultaneously space-time variational saddle point formulation, so involving both velocities u and pressure p. For the instationary Stokes problem, it is shown that the corresponding operator is a boundedly invertible linear mapping between H1 and H'2, both Hilbert spaces H1 and H2 being Cartesian products of (intersections of) Bochner spaces, or duals of those. Based on these results, the operator that corresponds to the Navier−Stokes...

Spatially-dependent and nonlinear fluid transport: coupling framework

Jürgen Geiser (2012)

Open Mathematics

We introduce a solver method for spatially dependent and nonlinear fluid transport. The motivation is from transport processes in porous media (e.g., waste disposal and chemical deposition processes). We analyze the coupled transport-reaction equation with mobile and immobile areas. The main idea is to apply transformation methods to spatial and nonlinear terms to obtain linear or nonlinear ordinary differential equations. Such differential equations can be simply solved with Laplace transformation...

Special finite-difference approximations of flow equations in terms of stream function, vorticity and velocity components for viscous incompressible liquid in curvilinear orthogonal coordinates

Harijs Kalis (1993)

Commentationes Mathematicae Universitatis Carolinae

The Navier-Stokes equations written in general orthogonal curvilinear coordinates are reformulated with the use of the stream function, vorticity and velocity components. The resulting system id discretized on general irregular meshes and special monotone finite-difference schemes are derived.

Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai

Haubold, Hans, Kumar, Dilip, Nair, Seema, Joseph, Dhannya (2010)

Fractional Calculus and Applied Analysis

The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information...

Spectral discretization of Darcy equations coupled with Navier-Stokes equations by vorticity-velocity-pressure formulation

Yassine Mabrouki, Jamil Satouri (2022)

Applications of Mathematics

We consider a model coupling the Darcy equations in a porous medium with the Navier-Stokes equations in the cracks, for which the coupling is provided by the pressure's continuity on the interface. We discretize the coupled problem by the spectral element method combined with a nonoverlapping domain decomposition method. We prove the existence of solution for the discrete problem and establish an error estimation. We conclude with some numerical tests confirming the results of our analysis.

Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem

Karima Amoura, Christine Bernardi, Nejmeddine Chorfi (2006)

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

We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical...

Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem

Karima Amoura, Christine Bernardi, Nejmeddine Chorfi (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical...

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