2021/04/12 by Rinaldo M. Colombo, Colombo, R. M., Graziano Guerra +3
Engineering · #35L65 #76N10 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2104.05548
openalex publication_date 2021/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.