Raphaël Paulus

Innovative modelling of 3D unsaturated flow in porous media by coupling independent models for vertical and lateral flows

Unsaturated groundwater flows are mathematically represented by the Richards equation. Hitherto, in Hydrology, solutions of this equation mainly serve as an alimentation of the source term for the surface runoff modelling. Therefore, the complete resolution of the 3D model looks surplus to requirements and the infiltration is dealt either thanks to 1D vertical modelling of the Richards equation or through derivate models (like e.g. the Green-Ampt infiltration model or the Horton law), thus ignoring eventual horizontal transfers. Nowadays, the request for more detailed information is real, and the physics of groundwater unsaturated flow needs to be represented more reliably. This information could be furnished by the resolution of the complete 3D model, but, although numerically mastered and well documented, it is very costly for large scale-both in time and space-real applications (climate change adaptation of watersheds). The authors propose an original solution decoupling the 3D equations into 1D vertical equations and a 2D depth-integrated horizontal equation. The aim is to consider independent vertical columns of infiltration coupled with lateral transfer of mass through the boundary conditions. On this basis, they postulate that the mass transfers in the three dimensions are correctly represented. This way problematic like the supply of the aquifers, the re-emergence of groundwater to surface water or especially the capability of memorization of past rainy events ...could be reliably depicted. The two coupled models are solved on a unique numerical frame. A cell-centred Finite Volume method is used to solve the parabolic partial differential equations. The spatial derivatives are approximate by a second order central difference scheme, while the time splitting follows an implicit backward Euler scheme coupled with Picard iteration. The method has been tested and its reliability assessed on different theoretical two-dimensional cross-sectional test cases representing infiltration phenomena.

Blood Flow under External Strains; Phenomenological Approach, Theoretical Developments & Numerical Analysis

In the medical field, the measurement of blood flow characteristics is often necessary. more specifically, blood pressure is an essential measure when it comes to assessing health. all over the world, many people suffer from hyper- or hypotension, and as it is known that these diseases can lead to serious complications, it is of great interest to determine the blood pressure with high accuracy. Nowadays, such information requires the use of specific materials; the present method for the measurement of the arterial pressure, by applying pressure using an armband (with a control device called sphygmomanometer), is known to introduce significant errors due to the inadequacy of the band dimensions (both the length and the circumference). The objective of the present research is to study and simulate the discharge of the blood in an artery subjected to external strains using theoretical developments and a numerical approach. Based on these modelling results, the response of the fluid to the external pressure of the band can be studied, and finally appropriate corrective factors for the true pressure and the measured pressure could be assessed. This research has been carried out with the aim of sharing medical and engineering views on the subject. The artery can be modelled as a deformable pipe, where the blood flowing in it is a fluid with specific properties. Thus, two complementary and interconnected domains are covered, solid mechanics (to obtain analytic relations between the strains and the deformations, using either linear or non-linear theories) and fluid mechanics (to study the discharge of blood in a deformable pipe, using finite volume methods), therefore considering the problem as a loose fluid–structure interaction (fSI). These two domains, which are well studied for common materials in civil engineering applications, are applied here not only to specific materials but especially to uncommon structures that, besides the somehow common fSI developments, lead to the investigation and research of very specific boundary conditions, giving them a physi cally based behaviour. at present, the research has reached the penultimate step, with the two main mentioned axes being fully developed and tested on their own. In particular, the boundary conditions developed for the models have been investigated and modelled in depth.

Computational Hemodynamics Coupled with Mechanical Behaviour of the Surrounded Materials, in the Specific Case of the Brachial Artery

Blood pressure is an essential measure when it comes to peoples’ health. All around the world a high number of people are suffering from hyperor low tension, and knowing that these diseases can lead to serious complications it is essential to measure blood pressure with high accuracy. The present methods for the measurement of the arterial pressure, by induction of a pressure through an armband (with a control device called sphygmomanometer) are known to introduce some significant errors. Those are caused partly by the inaccuracy and inadequacy of the armband and its dimensions (either the length or the circumference). The objective of the research presented in this paper is to study and simulate the discharge of the blood in the brachial artery. Based on these modelling results, the response of the fluid to the external pressure of the band can be obtained, and finally appropriate corrective factors between the true pressure and the read one could be assessed. From this perspective, research is carried out with the aim of sharing medical and engineering views on this subject. The artery can be modelled as a particular deformable pipe, when the blood is actually a fluid with specific properties. Thus the two complementary and interconnected domains are covered, so be it the solid mechanics (to obtain analytic relations between the strains and the deformations, using either linear or non-linear theories) and the fluid mechanics (to study the discharge of the blood considering a particular deformable pipe, using finite volume methods). Finally, many factors such as BC, for example, or other specific parameters have to be investigated deeply. In this paper, only the hydraulic results will be presented, discussed and analysed. The mechanical developments, being for now essentially analytical, will be mostly left out.