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A Discontinuous Galerkin Method for Blood Flow and Solute Transport in One-Dimensional Vessel Networks

Communications on Applied Mathematics and Computation 2022年第2期4卷 500-529页

作者： Rami Masri Charles Puelz Beatrice Riviere Department of Computational and Applied Mathematics Rice UniversityHoustonTX 77005USA Department of Pediatrics-Cardiology Baylor College of MedicineHoustonTX 77030USA

This paper formulates an efficient numerical method for solving the convection diffusion solute transport equations coupled to blood flow equations in vessel *** reduced coupled model describes the variations of vessel cross-sectional area,radially averaged blood momentum and solute concentration in large vessel *** the discretization of the reduced transport equation,we combine an interior penalty discontinuous Galerkin method in space with a novel locally implicit time stepping *** stability and the convergence are *** results show the impact of the choice for the steady-state axial velocity profile on the numerical solutions in a fifty-five vessel network with physiological boundary data.

关键词： Reduced models Blood flow Solute transport Coriolis coefficient Vessel networks junction conditions Locally implicit

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Supplement to the previous application of the first junction condition to a highly symmetric spacetime

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Chinese Physics B 2007年第12期16卷 3605-3609页

作者：覃一平 Center for Astrophysics Guangzhou University Guangzhou 510006 China National Astronomical Observatories/Yurman Observatory Chinese Academy of Sciences Kunming 650011 China Physics Department Guangxi University Nanning 530004 China

Application of the first junction condition to a highly symmetric spacetime was investigated recently in Chin. Phys. Left. B 546 189 2006, where a partial differential equation arising from the connection of the Robertson-Walker and the Schwarzschild-de Sitter metrics was presented, but no solutions of the equation were provided. Here we provide a proof to the statement that there exist solutions of the equation. In addition, an example of the solution and some analyses associated with this issue are presented. We find that in connecting the two metrics, there are three conditions which should be satisfied. Of these conditions, one condition constrains the place where the two metrics can take the same value for a local system whose mass is provided which marks the boundary of the system, and the other two constrain the transformation form. In realizing the connection of the two metrics, the latter two conditions are required to be satisfied only at the boundary defined by the former condition.

关键词： general relativity metrics junction conditions

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