publication . Article . Other literature type . Preprint . 2019

Geometric Theory of Flexible and Expandable Tubes Conveying Fluid: Equations, Solutions and Shock Waves

François Gay-Balmaz; Vakhtang Putkaradze;
Open Access
  • Published: 01 Apr 2019 Journal: Journal of Nonlinear Science, volume 29, pages 377-414 (issn: 0938-8974, eissn: 1432-1467, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
  • Country: France
Abstract
International audience; We present a theory for the three-dimensional evolution of tubes with expandable walls conveying fluid. Our theory can accommodate arbitrary deformations of the tube, arbitrary elasticity of the walls, and both compressible and incompressible flows inside the tube. We also present the theory of propagation of shock waves in such tubes and derive the conservation laws and Rankine-Hugoniot conditions in arbitrary spatial configuration of the tubes, and compute several examples of particular solutions. The theory is derived from a variational treatment of Cosserat rod theory extended to incorporate expandable walls and moving flow inside the...
Subjects
arXiv: Physics::Fluid Dynamics
free text keywords: General Engineering, Modelling and Simulation, Applied Mathematics, [MATH]Mathematics [math], [NLIN]Nonlinear Sciences [physics], Physics - Fluid Dynamics, Mathematics - Dynamical Systems, Nonlinear Sciences - Chaotic Dynamics, Compressibility, Geometric group theory, Spatial configuration, Fluid equation, Shock wave, Conservation law, Flow (psychology), Physics, Elasticity (economics), Mechanics
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