A Structure-Preserving Finite Volume Scheme for the Barotropic Euler System

K. R. Arun, IISER Thiruvananthapuram

Speaker	K. R. Arun, IISER Thiruvananthapuram
When	Aug 26, 2025 from 04:00 PM to 05:00 PM
Where	LH-111, First Floor
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COLLOQUIUM TALK

Abstract: We consider a semi-implicit in time, entropy-stable finite volume scheme for the compressible barotropic Euler system. We analyse its weak convergence to a dissipative measure-valued (DMV) solution of the continuous equations. The entropy stability is achieved by introducing a shifted velocity in the convective fluxes of the mass and momentum balances, provided that some CFL-like condition is satisfied. A consistency analysis is performed in the spirit of Lax’s equivalence theorem under some physically reasonable boundedness assumptions. K-convergence is used to obtain some strong convergence results, which are then illustrated via rigorous numerical case studies. The convergence of the scheme to a DMV solution, a weak solution, and a strong solution of the Euler system using the weak-strong uniqueness principle and relative entropy is presented.

Speaker Bio: K. R. Arun is a faculty member at the Indian Institute of Science Education and Research (IISER) Thiruvananthapuram, Kerala. He earned his Ph.D. in Mathematics from the Indian Institute of Science, Bangalore. He has worked at Institut fuer Geometrie und Praktische Mathematik, RWTH Aachen, Germany, and at the Institut fuer Numerische Simulation, Technische Universitaet Hamburg Harburg, Germany. His research interests include hyperbolic systems of conservation laws, asymptotic preserving schemes, genuinely multidimensional numerical schemes, nonlinear waves and shock waves.