Title of the talk: High-order Domain Invariant Numerical Schemes for Hyperbolic Balance Laws

Date & Time and Venue : 28 July 2025, 11:30 AM - 12:30 PM, Seminar Hall, Dept. of Mathematics.

Abstract: The systems of hyperbolic balance laws arise in several areas, especially in Computational Fluid Dynamics (CFD) and plasma flows. Due to lack of theory for the continuous problems, designing of stable numerical algorithms for the systems of hyperbolic balance laws is highly non-trivial. We are interested in high order numerical schemes for fluid flow and plasma flow models, which are robust. Robustness is achieved by designing positivity preserving numerical schemes. Positivity of the scheme is indeed desirable. Otherwise, we might lose the hyperbolicity of the system, and the solution produced by the numerical scheme will have no physical meaning. In particular, we consider the Discontinuous Galerkin method, finite difference method, and finite volume method. The WENO reconstructions are also used to get high order accuracy in finite difference and finite volume methods. The path-conservative schemes are used to tackle the non-conservative structure of the models. Here, we will discuss the construction of these numerical schemes for fluid flow and plasma flow models and their performance by numerical experiments.

About the Speaker: Dr. Asha Kumari Meena is currently working as an Assistant Professor in the Department of Mathematics at the Central University of Rajasthan. She earned her Ph.D. in Mathematics from I.I.T.  Delhi in 2018, followed by a post-doctoral research fellowship at the TIFR Centre for Applicable Mathematics in Bangalore. Her research interests lie in the areas of scientific computing for fluid and plasma flow models, traffic flow modeling, and numerical schemes such as finite volume, WENO, and discontinuous Galerkin methods.