A ‘well-balanced’ finite volume scheme for blood flow simulation. (English) Zbl 1455.76215
Summary: We are interested in simulating blood flow in arteries with a one-dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the Saint-Venant shallow water equations context) we will perform a simple finite volume scheme. We focus on conservation properties of this scheme, which were not previously considered. To emphasize the necessity of this scheme, we present how a too simple numerical scheme may induce spurious flows when the basic static shape of the radius changes. On the contrary, the proposed scheme is ‘well-balanced’: it preserves equilibria of \(Q=0\). Then examples of analytical or linearized solutions with and without viscous damping are presented to validate the calculations. The influence of abrupt change of basic radius is emphasized in the case of an aneurism.
MSC:
| 76Z05 | Physiological flows |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 92C35 | Physiological flow |
Keywords:
blood flow simulation; well-balanced scheme; finite volume scheme; hydrostatic reconstruction; man at eternal rest; semi-analytical solutions; shallow waterReferences:
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