I am working on pulsatile flow of blood in an artery with slightly elliptic cross section and landed up with Mathieu Functions. The computational complexity of dealing with continued fractions and recurrence relations poses a great threat. There are some classical work on these lines way back in 1950's but due to poor computational facility at that time, the authors have just provided mathematical solutions without carrying out any computational work to understand the flow characteristics. Any comments on this? References?
Here, in Brazil, we developed , in a Master Thesis, a pulsatile experimental set up based a piston system. Our work is experimental, this set up use a computer with a Interface Human Machine ( in C computer language) to control temperature, motor cycle, and measure pressure variation . If you want to make experimental test contact us.
It depends on what you are looking for, but the combined flow pulsations and pressure pulsations can be calculated/simulated by setting up the balance equations where the elliptical shape can be incorporated in the total compressibility (dVdp) of the fluid and the walls of the pipe/vessel. The dV/dp for an elliptically shaped pipe can be calculated in different ways. I have simulated the piston pipe induced flow an pressure in elliptically shaped stainless steel pipes in this way, where the elliptical contribution to the compressibility (dV/dP) was calculated by a colleague who used a FEM program for that.
Thanks a lot to all the three professors who have responded. I put on record my sincere thanks to Prof. Andriy O Boriysyuk for providing an URL to locate the answers to my question. Indeed, it is an excellent link with voluminous information.
Pulsatile Viscous Flows in Elliptical Vessels and Annuli: Solution to the Inverse Problem, with Application to Blood and Cerebrospinal Fluid Flow,
SIAM Journal on Applied Mathematics 74.1 (2014): 40-59.
I record my sincere thanks to Professor Kent-Andre Mardal for suggesting an earlier work. We are developing the program to directly deal with the solution obtained using Mathieu function. From the link provided by Prof.Andriy O Borisyuk also we got many inputs. Thanks a lot. I shall post here the progress, if any, we make in due course.
Continued fractions and branched continued fractions are objects of my research. Write please more detail your problems. I will help you with pleasure
Thank you Prof.Maria Bubniak. I shall contact you as and when I face problems in computing the continued fractions involved in the Mathieu Functions.
My e-mail [email protected].
That is why I wait more detail information about your problem. I hope I can help you
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