A BGK approximation to scalar conservation laws with discontinuous flux
Florent Berthelin (JAD), Julien Vovelle (ICJ)
TL;DR
This paper investigates a BGK approximation method for scalar conservation laws with discontinuous flux, proving well-posedness and convergence to the entropy solution as the relaxation parameter approaches zero.
Contribution
It introduces a BGK approximation framework for scalar conservation laws with discontinuous flux and establishes its convergence to the entropy solution.
Findings
Proves well-posedness of the BGK approximation for discontinuous flux
Shows convergence of the approximation to the entropy solution as relaxation parameter tends to zero
Provides a rigorous mathematical foundation for the approximation method
Abstract
We study the BGK approximation to first-order scalar conservation laws with a flux which is discontinuous in the space variable. We show that the Cauchy Problem for the BGK approximation is well-posed and that, as the relaxation parameter tends to 0, it converges to the (entropy) solution of the limit problem.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNavier-Stokes equation solutions · Fluid Dynamics and Turbulent Flows · Gas Dynamics and Kinetic Theory