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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 low Mach nuclear core model

Stéphane Dellacherie (2012)

ESAIM: Proceedings

We propose to formally derive a low Mach number model adapted to the modeling of a water nuclear core (e.g. of PWR- or BWR-type) in the forced convection regime or in the natural convection regime by filtering out the acoustic waves in the compressible Navier-Stokes system. Then, we propose a monodimensional stationary analytical solution with regular and singular charge loss when the equation of state is a stiffened gas equation. Moreover, we show...

On a model system for the oblique interaction of internal gravity waves

Jean-Claude Saut, Nikolay Tzvetkov (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We give local and global well-posedness results for a system of two Kadomtsev-Petviashvili (KP) equations derived by R. Grimshaw and Y. Zhu to model the oblique interaction of weakly nonlinear, two dimensional, long internal waves in shallow fluids. We also prove a smoothing effect for the amplitudes of the interacting waves. We use the Fourier transform restriction norms introduced by J. Bourgain and the Strichartz estimates for the linear KP group. Finally we extend the result of [3] for lower...

On a nonlocal problem for a confined plasma in a Tokamak

Weilin Zou, Fengquan Li, Boqiang Lv (2013)

Applications of Mathematics

The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms u * ' ( | u > u ( x ) | ) and | u > u ( x ) | , which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem.

On an evolutionary nonlinear fluid model in the limiting case

Stephan Luckhaus, Josef Málek (2001)

Mathematica Bohemica

We consider the two-dimesional spatially periodic problem for an evolutionary system describing unsteady motions of the fluid with shear-dependent viscosity under general assumptions on the form of nonlinear stress tensors that includes those with p -structure. The global-in-time existence of a weak solution is established. Some models where the nonlinear operator corresponds to the case p = 1 are covered by this analysis.

On boundary-driven time-dependent Oseen flows

Paul Deuring (2008)

Banach Center Publications

We consider the single layer potential associated to the fundamental solution of the time-dependent Oseen system. It is shown this potential belongs to L²(0,∞,H¹(Ω)³) and to H¹(0,∞,V') if the layer function is in L²(∂Ω×(0,∞)³). (Ω denotes the complement of a bounded Lipschitz set; V denotes the set of smooth solenoidal functions in H¹₀(Ω)³.) This result means that the usual weak solution of the time-dependent Oseen function with zero initial data and zero body force may be represented by a single...

On caustics associated with Rossby waves

Arthur D. Gorman (1996)

Applications of Mathematics

Rossby wave equations characterize a class of wave phenomena occurring in geophysical fluid dynamics. One technique useful in the analysis of these waves is the geometrical optics, or multi-dimensional WKB technique. Near caustics, e.g., in critical regions, this technique does not apply. A related technique that does apply near caustics is the Lagrange Manifold Formalism. Here we apply the Lagrange Manifold Formalism to study Rossby waves near caustics.

On caustics associated with the linearized vorticity equation

Petya N. Ivanova, Arthur D. Gorman (1998)

Applications of Mathematics

The linearized vorticity equation serves to model a number of wave phenomena in geophysical fluid dynamics. One technique that has been applied to this equation is the geometrical optics, or multi-dimensional WKB technique. Near caustics, this technique does not apply. A related technique that does apply near caustics is the Lagrange Manifold Formalism. Here we apply the Lagrange Manifold Formalism to determine an asymptotic solution of the linearized vorticity equation and to study associated wave...

On evolution Galerkin methods for the Maxwell and the linearized Euler equations

Mária Lukáčová-Medviďová, Jitka Saibertová, Gerald G. Warnecke, Yousef Zahaykah (2004)

Applications of Mathematics

The subject of the paper is the derivation and analysis of evolution Galerkin schemes for the two dimensional Maxwell and linearized Euler equations. The aim is to construct a method which takes into account better the infinitely many directions of propagation of waves. To do this the initial function is evolved using the characteristic cone and then projected onto a finite element space. We derive the divergence-free property and estimate the dispersion relation as well. We present some numerical...

On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions

Miroslav Bulíček, Roger Lewandowski, Josef Málek (2011)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we establish the large-data and long-time existence of a suitable weak solution to an initial and boundary value problem driven by a system of partial differential equations consisting of the Navier-Stokes equations with the viscosity ν polynomially increasing with a scalar quantity k that evolves according to an evolutionary convection diffusion equation with the right hand side ν ( k ) | 𝖣 ( v → ) | 2 that is merely L 1 -integrable over space and time. We also formulate a conjecture concerning regularity...

On global solutions to a nonlinear Alfvén wave equation

XS. Feng, F. Wei (1995)

Annales Polonici Mathematici

We establish the global existence and uniqueness of smooth solutions to a nonlinear Alfvén wave equation arising in a finite-beta plasma. In addition, the spatial asymptotic behavior of the solution is discussed.

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