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Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry and in vivo stress incorporation

Joris BolsJoris DegrooteBram TrachetBenedict VerhegghePatrick SegersJan Vierendeels — 2013

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

visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to conditions. This entails an internal stress state to be present in the measured geometry of a blood vessel due to the presence of the blood pressure. In order to correct for this stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the stress field...

Modelling of natural convection flows with large temperature differences : a benchmark problem for low Mach number solvers. Part 1. Reference solutions

Patrick Le QuéréCatherine WeismanHenri PaillèreJan VierendeelsErik DickRoland BeckerMalte BraackJames Locke — 2005

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

There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of...

Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 1. Reference Solutions

Patrick Le QuéréCatherine WeismanHenri PaillèreJan VierendeelsErik DickRoland BeckerMalte BraackJames Locke — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference...

Modelling of natural convection flows with large temperature differences : a benchmark problem for low Mach number solvers. Part 2. Contributions to the June 2004 conference

Henri PaillèrePatrick Le QuéréCatherine WeismanJan VierendeelsErik DickMalte BraackFrédéric DabbeneAlberto BeccantiniEtienne StuderThibaud KloczkoChristophe CorreVincent HeuvelineMasoud DarbandiSeyed Farid Hosseinizadeh — 2005

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

In the second part of the paper, we compare the solutions produced in the framework of the conference “Mathematical and numerical aspects of low Mach number flows” organized by INRIA and MAB in Porquerolles, June 2004, to the reference solutions described in Part 1. We make some recommendations on how to produce good quality solutions, and list a number of pitfalls to be avoided.

Modelling of Natural Convection Flows with Large Temperature Differences: A Benchmark Problem for Low Mach Number Solvers. Part 2. Contributions to the June 2004 conference

In the second part of the paper, we compare the solutions produced in the framework of the conference “Mathematical and numerical aspects of low Mach number flows” organized by INRIA and MAB in Porquerolles, June 2004, to the reference solutions described in Part 1. We make some recommendations on how to produce good quality solutions, and list a number of pitfalls to be avoided.

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