Non Conservative Products in Fluid Dynamics
2021
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.
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