Non Conservative Products in Fluid Dynamics
Analysis of PDEs
2021-04-13 v1 Mathematical Physics
math.MP
Abstract
Fluid flow in pipes with discontinuous cross section or with kinks is described through balance laws with a non conservative product in the source. At jump discontinuities in the pipes' geometry, the physics of the problem suggests how to single out a solution. On this basis, we present a definition of solution for a general BV geometry and prove an existence result, consistent with a limiting procedure from piecewise constant geometries. In the case of a smoothly curved pipe we thus justify the appearance of the curvature in the source term of the linear momentum equation. These results are obtained as consequences of a general existence result devoted to abstract balance laws with non conservative source terms.
Cite
@article{arxiv.2104.05548,
title = {Non Conservative Products in Fluid Dynamics},
author = {R. M. Colombo and G. Guerra and Y. Holle},
journal= {arXiv preprint arXiv:2104.05548},
year = {2021}
}