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.

中文翻译：

---

一种计算二叉分叉树中平稳流的算法

摘要 在这项工作中，我们提出了一种用于计算分叉树中平稳流的算法。我们的想法是将树分成更小的基本块，每个块对应一个分叉，并为各个块解决一系列流问题。数值实验表明该算法运行良好。我们给出了一个可以通过数值验证的收敛标准，以及一个重要特殊情况的解析收敛证明。我们想到的应用是计算人体动脉树中随时间变化的血流量。这里介绍的工作是针对一个简化的案例，但我们讨论了将我们的工作扩展到现实案例。还讨论了潜在的应用。