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Analytical study of Pavlov equation

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ADIW01 - Layering — A structure formation mechanism in oceans, atmospheres, active fluids and plasmas

The study of the complexity of fluid dynamics has attracted many researchers and CFD analyst over the years. A wide variety of engineering systems can be modeled and expressed in the language of differential equations. Therefore, understanding the solution of these PDEs has always played a significant role in science and engineering research. The hyperbolic conservation law is an important class of time dependent PDEs arising in a wide spectrum of disciplines such as gas dynamics, fluid dynamics, acoustics, biomechanics and geophysics. Because of the possibility of discontinuity and sharp gradients in the solutions, the majority of these hyperbolic PDEs are solved using numerical methods. The main difficulties in the numerical methods are stability, convergence analysis and round-off errors. The effect of round off errors may lead to approximate solutions. Hence, the convergence to the correct solution and its accuracy needs to be ascertained. Therefore, it is of fundamental importance to develop accurate methods such as analytic or semi-analytical techniques to obtain a precise solution of hyperbolic conservation equations. The development of methods for finding an accurate solution of hyperbolic conservation equations is significant to simulate and predict their behavior. Hence, presents the semi-analytical based homotopy analysis method (HAM) for solving the nonlinear hyperbolic PDEs. The conservation equations such as the Pavlov equation, Burgers equation, and Euler equations of gas dynamics would be considered for investigations. It is envisaged to solve these equations using the HAM . The present work will provide the synthesis in the direction of understanding HAM combined with the method of characteristics approach to examine Pavlov equation, known for associated commuting flows.

This talk is part of the Isaac Newton Institute Seminar Series series.

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