By Tomáš Bodnár, Giovanni P. Galdi, Šárka Nečasová
This publication offers, in a methodical method, up-to-date and complete descriptions and analyses of a few of the main suitable difficulties within the context of fluid-structure interplay (FSI). mostly talking, FSI is one of the hottest and exciting difficulties in technologies and contains commercial in addition to organic functions. quite a few basic elements of FSI are addressed from various views, with a spotlight on biomedical functions. extra particularly, the e-book provides a mathematical research of uncomplicated questions just like the well-posedness of the correct preliminary and boundary price difficulties, in addition to the modeling and the numerical simulation of a couple of primary phenomena relating to human biology. those latter learn themes comprise blood move in arteries and veins, blood coagulation and speech modeling.
We think that the diversity of the themes mentioned, in addition to the various ways used to handle and remedy the corresponding difficulties, may also help readers to increase a extra holistic view of the most recent findings at the topic, and of the appropriate open questions. for a similar cause we think the publication to develop into a depended on better half for researchers from assorted disciplines, reminiscent of arithmetic, physics, mathematical biology, bioengineering and medicine.
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This ebook provides, in a methodical approach, up-to-date and accomplished descriptions and analyses of a few of the main correct difficulties within the context of fluid-structure interplay (FSI). regularly talking, FSI is one of the hottest and fascinating difficulties in technologies and contains commercial in addition to organic purposes.
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Extra info for Fluid-Structure Interaction and Biomedical Applications
T; x//. Note here that we have written the forcing term thanks to a change of variables depending on the given h. 80), cf. 98) We will show later that the approximation with Ä is reasonable. One of the possible physical interpretations for introducing finite Ä comes from the mathematical modeling of semi-pervious boundary, where this type of boundary condition occurs. In our case, the boundary † seems to be partly permeable for finite Ä, but letting Ä ! 1 it becomes impervious. In fact, we prove the existence of solution if Ä !
1 C Á/ D 0. 0; T //2 g > 0. But 28 C. Grandmont et al. TkC1 Tk k =2 and goes to zero, which is a contradiction. This achieves the proof of existence of a weak solution as long as no contact occurs between the elastic structure and the bottom of the fluid cavity. Undamped Wave Equation: ˇ2 ! 0 We explain in this subsection how one can pass to the limit in the coupled problem as the structure viscosity ˇ2 goes to zero. As we will see, the fluid dissipation enables to control the space of high frequencies of the structure velocity without any added viscosity on the wave equation.
The goal is to underline the possible links between 32 C. Grandmont et al. existence of solutions and numerical schemes. In particular we will see in Sect. 3 a semi-implicit scheme based on the same kind of splitting ideas. 12) and with no external forces applied to the coupled system. For the fluid boundary conditions one could assume that the fluid velocity satisfies Dirichlet homogeneous boundary conditions as in  or considers periodicity in the x variable as it is done in . Note that this periodicity assumption seems to be necessary in the case where D 0.