Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session J15: CFD: Shock Capturing, DG, Higher Order Schemes
4:35 PM–6:32 PM,
Sunday, November 19, 2023
Room: 144C
Chair: Upendra Bhandarkar, Indian Institute of Technology Bombay
Abstract: J15.00008 : Information geometric regularization of the barotropic Euler equation
6:06 PM–6:19 PM
Presenter:
Florian Schaefer
(Georgia Institute of Technology)
Authors:
Florian Schaefer
(Georgia Institute of Technology)
Ruijia Cao
(Georgia Institute of Technology)
We revisit this classical problem by interpreting the Euler equations as flows on diffeomorphism manifolds based on the pioneering work of Vladimir Arnold. From this perspective, the formation of shock waves results from the lack of geodesic completeness of the diffeomorphism manifold. We restore the geodesic completeness of the diffeomorphism manifold by embedding it into a suitable information geometry. By deriving the Euler equations on this modified geometry, we obtain a regularization that avoids the formation of singularities without adding viscosity.
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