Displaying similar documents to “A reduced model for Darcy’s problem in networks of fractures”

Mathematical and Numerical Analysis of an Alternative Well-Posed Two-Layer Turbulence Model

Bijan Mohammadi, Guillaume Puigt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this article, we wish to investigate the behavior of a two-layer turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations. First, we explain the difficulties inherent in the model. Then, we present a new variable that enables the mathematical study. Due to a problem of definition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some...

An anti-diffusive Lagrange-Remap scheme for multi-material compressible flows with an arbitrary number of components

Marie Billaud Friess, Samuel Kokh (2012)

ESAIM: Proceedings

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We propose a method dedicated to the simulation of interface flows involving an arbitrary number of compressible components. Our task is two-fold: we first introduce a -component flow model that generalizes the two-material five-equation model of [2,3]. Then, we present a discretization strategy by means of a Lagrange-Remap [8,10] approach following the lines of [5,7,12]. The projection step involves an anti-dissipative mechanism derived from [11,12]. This feature allows to prevent...

Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

Sansuke M. Watanabe, Pablo J. Blanco, Raúl A. Feijóo (2013)

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

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A distributed-parameter (one-dimensional) anatomically detailed model for the arterial network of the arm is developed in order to carry out hemodynamics simulations. This work focuses on the specific aspects related to the model set-up. In this regard, stringent anatomical and physiological considerations have been pursued in order to construct the arterial topology and to provide a systematic estimation of the involved parameters. The model comprises 108 arterial segments, with 64...

Mathematical Model of Fibrin Polymerization

A.I. Lobanov, A.V. Nikolaev, T.K. Starozhilova (2011)

Mathematical Modelling of Natural Phenomena

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Blood clotting system (BCS) modelling is an important issue with a plenty of applications in medicine and biophysics. The BCS main function is to form a localized clot at the site of injury preventing blood loss. Mutual influence of fibrin clot consisting mainly of fibrin polymer gel and blood flow is an important factor for BCS to function properly. The process of fibrin polymer mesh formation has not adequately been described by current mathematical models. That is why it is not possible...

Automatic simplification of Darcy’s equations with pressure dependent permeability

Etienne Ahusborde, Mejdi Azaïez, Faker Ben Belgacem, Christine Bernardi (2013)

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

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We consider the flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with mixed boundary conditions. Since the boundary pressure can present high variations, the permeability of the medium also depends on the pressure, so that the model is nonlinear. estimates allow us to omit this dependence where the pressure does not vary too much. We perform the numerical analysis of a spectral element discretization of the simplified model. Finally we propose a strategy...

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

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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.

Experimental comparison of traffic flow models on traffic data

Horňák, Ivan, Přikryl, Jan

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Despite their deficiencies, continuous second-order traffic flow models are still commonly used to derive discrete-time models that help traffic engineers to model and predict traffic oflow behaviour on highways. We brie fly overview the development of traffic flow theory based on continuous flow-density models of Lighthill-Whitham-Richards (LWR) type, that lead to the second-order model of Aw-Rascle. We will then concentrate on widely-adopted discrete approximation to the LWR model...

Blood Flow Simulation in Atherosclerotic Vascular Network Using Fiber-Spring Representation of Diseased Wall

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

Mathematical Modelling of Natural Phenomena

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We present the fiber-spring elastic model of the arterial wall with atherosclerotic plaque composed of a lipid pool and a fibrous cap. This model allows us to reproduce pressure to cross-sectional area relationship along the diseased vessel which is used in the network model of global blood circulation. Atherosclerosis attacks a region of systemic arterial network. Our approach allows us to examine the impact of the diseased region onto...