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A HYPERBOLIC SYSTEM OF CONSERVATION LAWS FOR FLUID FLOWS THROUGH COMPLIANT AXISYMMETRIC VESSELS |
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| Authors: | Gui-Qiang GChen School of Mathematical Sciences Fudan University Shanghai China Mathematical Institute University of Oxford - St Giles Oxford OX LB UK |
| Institution: | [1]School of Mathematical Sciences, Fudan University, Shanghai 200433, China [2]Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford, OX1 3LB, UK [3]Department of Mathematics, Northwestern University, Evanston, IL 60208-2730, USA [4]Department of Mathematics, Computer Science and Statistics, Purdue University Calumet, Hammond, IN 46323-2094, USA |
| Abstract: | We are concerned with the derivation and analysis of one-dimensional hyperbolic systems of conservation laws modelling fluid flows such as the blood flow through compliant axisymmetric vessels.Early models derived are nonconservative and/or nonhomogeneous with measure source terms,which are endowed with infinitely many Riemann solutions for some Riemann data.In this paper,we derive a one-dimensional hyperbolic system that is conservative and homogeneous.Moreover,there exists a unique global Riemann solution for the Riemann problem for two vessels with arbitrarily large Riemann data,under a natural stability entropy criterion.The Riemann solutions may consist of four waves for some cases.The system can also be written as a 3 × 3 system for which strict hyperbolicity fails and the standing waves can be regarded as the contact discontinuities corresponding to the second family with zero eigenvalue. |
| Keywords: | conservation laws hyperbolic system fluid flow blood flow vessel hyperbolicity Riemann problem Riemann solution wave curve shock wave rarefaction wave standing wave stability |
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