Simulation of one‐dimensional blood flow in networks of human vessels using a novel TVD scheme

An extension of a total variation diminishing (TVD) scheme to solve one-dimensional (1D) blood flow for human circulation is proposed. This method is simple as it involves only a few modifications to existing shock-capturing TVD schemes. We have applied the method to a wide range of test cases including a complete simulation of the human vascular network. Excellent solutions have been demonstrated for problems involving varying and discontinuous mechanical properties of blood vessels. For 1D network simulations, the method has been shown to agree well with the reported computational results. Finally, the method has been demonstrated to compare favorably with in vivo experiments set up to study the impact of circle of Willis anomalies on flow patterns in the cerebral arterial system.

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