An algorithm for computing a stationary flow in a binary bifurcation tree

TitleAn algorithm for computing a stationary flow in a binary bifurcation tree
Publication TypeJournal Article
Year of Publication2021
AuthorsGodwinKakuba,, Berntsson, F, VladimirKozlov,
JournalApplied Numerical Mathematics
Volume159
Pagination125-137
Date Published January 2021
KeywordsBifurcation treeFixed point iterationFlow simulationConvergence proofNumerical examplesBlood circulation
Abstract

In this work we propose an algorithm for computing a stationary flow in a bifurcation tree. Our idea is to divide the tree into smaller basic blocks, each corresponding to one bifurcation, and solve a sequence of flow problems for the individual blocks. Numerical experiments demonstrate that the algorithm works well. We give a criteria for convergence that can be verified numerically and also an analytical convergence proof for an important special case.
The application we have in mind is the computation of the time dependent blood flow in the arterial tree of the human body. The work presented here is for a simplified case but we discuss the extension of our work to the realistic cases. Also potential applications are discussed.

URLhttps://www.sciencedirect.com/science/article/abs/pii/S016892742030252X
DOI10.1016/j.apnum.2020.08.017