A Roe type energy balanced solver for 1D arterial blood flow and transport. (English) Zbl 1390.76941
Summary: The approximate solver presented in this work is based on the upwind discretization of the source terms and a genuinely Roe solver for the one-dimensional blood flow equations in arteries. This augmented solver involves the presence of the source terms, ensuring convergence to the exact solution by including an extra wave associated to the change in the material properties and the friction term. The resulting numerical scheme is energy-balanced, that is, ensures equilibrium in rest conditions and is able to ensure numerically a constant level of energy in steady cases with velocity. The resulting numerical solver allows simulating directly mass transport without creating non-physical oscillations. The numerical scheme is assessed using steady and unsteady problems with exact solutions and is compared with models of the systemic arterial tree published in literature.
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 |
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