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Transport of pollutant in shallow water : a two time steps kinetic method

Emmanuel Audusse, Marie-Odile Bristeau (2003)

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

The aim of this paper is to present a finite volume kinetic method to compute the transport of a passive pollutant by a flow modeled by the shallow water equations using a new time discretization that allows large time steps for the pollutant computation. For the hydrodynamic part the kinetic solver ensures – even in the case of a non flat bottom – the preservation of the steady state of a lake at rest, the non-negativity of the water height and the existence of an entropy inequality. On an other...

Transport of Pollutant in Shallow Water A Two Time Steps Kinetic Method

Emmanuel Audusse, Marie-Odile Bristeau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to present a finite volume kinetic method to compute the transport of a passive pollutant by a flow modeled by the shallow water equations using a new time discretization that allows large time steps for the pollutant computation. For the hydrodynamic part the kinetic solver ensures – even in the case of a non flat bottom – the preservation of the steady state of a lake at rest, the non-negativity of the water height and the existence of an entropy inequality. On an other...

Two Numerical Methods for the elliptic Monge-Ampère equation

Jean-David Benamou, Brittany D. Froese, Adam M. Oberman (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The numerical solution of the elliptic Monge-Ampère Partial Differential Equation has been a subject of increasing interest recently [Glowinski, in 6th International Congress on Industrial and Applied Mathematics, ICIAM 07, Invited Lectures (2009) 155–192; Oliker and Prussner, Numer. Math.54 (1988) 271–293; Oberman, Discrete Contin. Dyn. Syst. Ser. B10 (2008) 221–238; Dean and Glowinski, in Partial differential equations, Comput. Methods Appl. Sci. 16 (2008) 43–63; Glowinski et al., Japan...

Uniform stabilization of a viscous numerical approximation for a locally damped wave equation

Arnaud Münch, Ademir Fernando Pazoto (2007)

ESAIM: Control, Optimisation and Calculus of Variations

This work is devoted to the analysis of a viscous finite-difference space semi-discretization of a locally damped wave equation in a regular 2-D domain. The damping term is supported in a suitable subset of the domain, so that the energy of solutions of the damped continuous wave equation decays exponentially to zero as time goes to infinity. Using discrete multiplier techniques, we prove that adding a suitable vanishing numerical viscosity term leads to a uniform (with respect to the mesh size)...

Variational analysis for the Black and Scholes equation with stochastic volatility

Yves Achdou, Nicoletta Tchou (2002)

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

We propose a variational analysis for a Black and Scholes equation with stochastic volatility. This equation gives the price of a European option as a function of the time, of the price of the underlying asset and of the volatility when the volatility is a function of a mean reverting Orstein-Uhlenbeck process, possibly correlated with the underlying asset. The variational analysis involves weighted Sobolev spaces. It enables to prove qualitative properties of the solution, namely a maximum principle...

Variational Analysis for the Black and Scholes Equation with Stochastic Volatility

Yves Achdou, Nicoletta Tchou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a variational analysis for a Black and Scholes equation with stochastic volatility. This equation gives the price of a European option as a function of the time, of the price of the underlying asset and of the volatility when the volatility is a function of a mean reverting Orstein-Uhlenbeck process, possibly correlated with the underlying asset. The variational analysis involves weighted Sobolev spaces. It enables to prove qualitative properties of the solution, namely a maximum principle...

Vessel Wall Models for Simulation of Atherosclerotic Vascular Networks

Yu. Vassilevski, S. Simakov, V. Salamatova, Yu. Ivanov, T. Dobroserdova (2011)

Mathematical Modelling of Natural Phenomena

There are two mathematical models of elastic walls of healthy and atherosclerotic blood vessels developed and studied. The models are included in a numerical model of global blood circulation via recovery of the vessel wall state equation. The joint model allows us to study the impact of arteries atherosclerotic disease of a set of arteries on regional haemodynamics.

Vorticity dynamics and numerical resolution of Navier-Stokes equations

Matania Ben-Artzi, Dalia Fishelov, Shlomo Trachtenberg (2001)

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

We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical data...

Vorticity dynamics and numerical Resolution of Navier-Stokes Equations

Matania Ben-Artzi, Dalia Fishelov, Shlomo Trachtenberg (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical data...

Currently displaying 381 – 400 of 419