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Flow in Collapsible Tubes with Discontinuous Mechanical Properties:Mathematical Model and Exact Solutions

Communications in Computational Physics 2013年第2期13卷 361-385页

作者： Eleuterio F.Toro annunziato siviglia Laboratory of applied Mathematics University of TrentoVia Mesiano 77I-38100 TrentoItaly

We formulate a one-dimensional time-dependent non-linear mathematical model for some types of physiological fluid flow in collapsible tubes with discontinuous material *** resulting 6×6 hyperbolic system is analysed and the associated Riemann problem is solved *** the solution algorithm deals with idealised cases,it is nonetheless uniquely well-suited for assessing the performance of numerical methods intended for simulating more general ***,our model may be a useful starting point for numerical calculations of realistic flows involving rapid and discontinuous material property *** important example in mind is the simulation of blood flow in medium-to-large veins in ***,we also discuss some peculiarities of the model regarding the loss of strict hyperbolicity and *** particular we show an example in which the solution of the Riemann problem is non unique.

关键词： Collapsible tubes physiological flows blood flows Riemann problem

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A Finite Volume Upwind-Biased Centred Scheme for Hyperbolic Systems of Conservation Laws:Application to Shallow Water Equations

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Communications in Computational Physics 2012年第9期12卷 1183-1214页

作者： Guglielmo Stecca annunziato siviglia Eleuterio F.Toro Department of Civil and Environmental Engineering University of TrentoVia Mesiano 77I-38100 TrentoItaly Laboratory of AppliedMathematics University of TrentoVia Mesiano 77I-38100 TrentoItaly.

We construct a new first-order central-upwind numerical method for solving systems of hyperbolic equations in conservative *** applies in multidimensional structured and unstructured *** proposed method is an extension of the UFORCEmethod developed by Stecca,siviglia and Toro[25],in which the upwind bias for the modification of the staggered mesh is evaluated taking into account the smallest and largest wave of the entire Riemann *** proposed first-order method is shown to be identical to the Godunov upwindmethod in applications to a 2×2 linear hyperbolic *** method is then extended to non-linear systems and its performance is assessed by solving the two-dimensional inviscid shallow water *** to second-order accuracy is carried out using an ADER-WENO approach in the finite volume framework on unstructured ***,numerical comparison with current competing numerical methods enables us to identify the salient features of the proposed method.

关键词： Conservative hyperbolic systems centred schemes unstructured meshes numerical fluxes shallow water equations FORCE upwind-biased

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