Non Conservative Products in Fluid Dynamics

arXiv (Cornell University)

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.

Authors 3

1. Rinaldo M. Colombo

   University of Brescia · Istituto Nazionale di Alta Matematica Francesco Severi

   Affiliation as printed

   INdAM Unit & Department of Information Engineering , University of Brescia , via Branze , 38 , 25123 Brescia , Italy

2. Graziano Guerra

   University of Milano-Bicocca

   Affiliation as printed

   Università degli Studi di Milano Bicocca , Dipartimento di Matematica e Applicazioni , via R. Cozzi , 55 , 20126 Milano , Italy

3. Yannick Holle Aachen Institut für Mathematik

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Institut für Mathematik , Templergraben 55 , 52062 Aachen , Germany