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Displaying 61 – 80 of 118

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

On reflection of shock front in multidimensional space

Chen Shuxing (1987/1988)

Séminaire Équations aux dérivées partielles (Polytechnique)

On the anomalous singularities of the solutions to some classes of weakly hyperbolic semilinear systems. Examples

Petar Popivanov, Iordan Iordanov (2003)

Banach Center Publications

This paper deals with the newly observed singularities of the solutions of some specific examples of weakly hyperbolic semilinear systems in R². Two, respectively three, characteristics are supposed to be mutually tangential at the origin only and the initial data are continuous only. The exact strength of the new-born singularities is investigated too.

On the existence of shock propagation in a flow through deformable porous media

E. Comparini, M. Ughi (2002)

Bollettino dell'Unione Matematica Italiana

We consider a one-dimensional incompressible flow through a porous medium undergoing deformations such that the porosity and the hydraulic conductivity can be considered to be functions of the flux intensity. The medium is initially dry and we neglect capillarity, so that a sharp wetting front proceeds into the medium. We consider the open problem of the continuation of the solution in the case of onset of singularities, which can be interpreted as a local collapse of the medium, in the general...

On the nonhamiltonian character of shocks in 2-D pressureless gas

Yu. G. Rykov (2002)

Bollettino dell'Unione Matematica Italiana

The paper deals with the 2-D system of gas dynamics without pressure which was introduced in 1970 by Ua. Zeldovich to describe the formation of largescale structure of the Universe. Such system occurs to be an intermediate object between the systems of ordinary differential equations and hyperbolic systems of PDE. The main its feature is the arising of singularities: discontinuities for velocity and d-functions of various types for density. The rigorous notion of generalized solutions in terms of...

On the sign of Colombeau functions and applications to conservation laws

Jiří Jelínek, Dalibor Pražák (2009)

Commentationes Mathematicae Universitatis Carolinae

A generalized concept of sign is introduced in the context of Colombeau algebras. It extends the sign of the point-value in the case of sufficiently regular functions. This concept of generalized sign is then used to characterize the entropy condition for discontinuous solutions of scalar conservation laws.