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SUMMARY:Analytical study of Pavlov equation - Mittu Walia (Indian Institut
 e of Technology)
DTSTART:20240115T154500Z
DTEND:20240115T161500Z
UID:TALK208459@talks.cam.ac.uk
DESCRIPTION:The study of the complexity of fluid dynamics has attracted ma
 ny researchers and CFD analyst over the years. A wide variety of engineeri
 ng systems can be modeled and expressed in the language of differential eq
 uations. Therefore\, understanding the solution of these PDEs has always p
 layed a significant role in science and engineering research. The hyperbol
 ic conservation law is an important class of time dependent PDEs arising i
 n a wide spectrum of disciplines such as gas dynamics\, fluid dynamics\, a
 coustics\, biomechanics and geophysics. Because of the possibility of disc
 ontinuity and sharp gradients in the solutions\, the majority of these hyp
 erbolic PDEs are solved using numerical methods. The main difficulties in 
 the numerical methods are stability\, convergence analysis and round-off e
 rrors. The effect of round off errors may lead to approximate solutions. H
 ence\, the convergence to the correct solution and its accuracy needs to b
 e ascertained. Therefore\, it is of fundamental importance to develop accu
 rate methods such as analytic or semi-analytical techniques to obtain a pr
 ecise solution of hyperbolic conservation equations. The development of me
 thods for finding an accurate solution of hyperbolic conservation equation
 s is significant to simulate and predict their behavior. Hence\, presents 
 the semi-analytical based homotopy analysis method (HAM) for solving the n
 onlinear hyperbolic PDEs. The conservation equations such as the Pavlov eq
 uation\, Burgers equation\, and Euler equations of gas dynamics would be c
 onsidered for investigations. It is envisaged to solve these equations usi
 ng the HAM. The present work will provide the synthesis in the direction o
 f understanding HAM combined with the method of characteristics approach t
 o examine Pavlov equation\, known for associated commuting flows.
LOCATION:Seminar Room 1\, Newton Institute
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