Harihara Maharna

Harihara Maharna

Applied Mathematics PhD Student at the University of Notre Dame

An Asymptotic Preserving and Energy Stable Scheme for the Euler System with Congestion Constraint

Project, Indian Institute of Science Education and Research (IISER), Thiruvananthapuram, Department of Mathematics, 2024

  • Guide: Dr. K. R. Arun, School of Mathematics, IISER Thiruvananthapuram, India
  • About the project: This work was conducted as part of my Master’s thesis at IISER Thiruvananthapuram.
    • In this project, we designed and analyzed a finite volume scheme for the barotropic Euler equations with the congestion pressure law and performed the singular limit termed as the hard congestion limit at the discrete level.
    • The developed scheme was an entropy stable and asymptotic preserving. We also obtained a-priori estimates on the relevant unknowns. We lastly, proved the efficiency of the numerical scheme by testing various numerical examples.