Compressible Navier-Stokes Equations in a Polyhedral Cylinder with Inflow Boundary Condition

Compressible Navier-Stokes Equations in a Polyhedral Cylinder with Inflow Boundary Condition In this paper our concern is with singularity and regularity of the compressible flows through a non-convex edge in $${\mathbb {R}}^3$$ R 3 . The flows are governed by the compressible Navies-Stokes equations on the infinite cylinder that has the non-convex edge on the inflow boundary. We split the edge singularity by the Poisson problem from the velocity vector and show that the remainder is twice differentiable while the edge singularity is observed to be propagated into the interior of the cylinder by the transport character of the continuity equation. An interior surface layer starting at the edge is generated and not Lipshitz continuous due to the singularity. The density function shows a very steep change near the interface and its normal derivative has a jump discontinuity across there. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Fluid Mechanics Springer Journals

Compressible Navier-Stokes Equations in a Polyhedral Cylinder with Inflow Boundary Condition

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Physics; Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics
ISSN
1422-6928
eISSN
1422-6952
D.O.I.
10.1007/s00021-017-0336-3
Publisher site
See Article on Publisher Site

Abstract

In this paper our concern is with singularity and regularity of the compressible flows through a non-convex edge in $${\mathbb {R}}^3$$ R 3 . The flows are governed by the compressible Navies-Stokes equations on the infinite cylinder that has the non-convex edge on the inflow boundary. We split the edge singularity by the Poisson problem from the velocity vector and show that the remainder is twice differentiable while the edge singularity is observed to be propagated into the interior of the cylinder by the transport character of the continuity equation. An interior surface layer starting at the edge is generated and not Lipshitz continuous due to the singularity. The density function shows a very steep change near the interface and its normal derivative has a jump discontinuity across there.

Journal

Journal of Mathematical Fluid MechanicsSpringer Journals

Published: Jul 14, 2017

References

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