In this paper, we develop parameter-robust numerical algorithms for Biot model and apply the algorithms in brain edema simulations. By introducing an intermediate variable, we derive a multiphysics reformulation of the Biot model. Based on the reformulation, the Biot model is viewed as a generalized Stokes subproblem combining with a reaction-diffusion subproblem. Solving the two subproblems together or separately leads to a coupled or a decoupled algorithm. We conduct extensive numerical experiments to show that the two algorithms are robust with respect to the key physical parameters. The algorithms are applied to study the brain swelling caused by abnormal accumulation of cerebrospinal fluid in injured areas. The effects of the key physical parameters on brain swelling are carefully investigated. It is observed that the permeability has the biggest influence on intracranial pressure (ICP) and tissue deformation; the Young's modulus and the Poisson ratio do not affect the maximum value of ICP too much but have big influence on the tissue deformation and the developing speed of brain swelling.

中文翻译：

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Biot模型的参数鲁棒多物理场算法在脑水肿模拟中的应用

在本文中，我们为 Biot 模型开发了参数稳健的数值算法，并将这些算法应用于脑水肿模拟。通过引入一个中间变量，我们推导出了 Biot 模型的多物理场重构。基于重新表述，Biot 模型被视为与反应扩散子问题相结合的广义斯托克斯子问题。一起或单独解决两个子问题会导致耦合或解耦算法。我们进行了大量的数值实验，以表明这两种算法在关键物理参数方面是稳健的。该算法用于研究因脑脊液异常积聚在受伤部位引起的脑肿胀。仔细研究了关键物理参数对脑肿胀的影响。观察到渗透性对颅内压（ICP）和组织变形的影响最大；杨氏模量和泊松比对ICP的最大值影响不大，但对组织变形和脑肿胀的发展速度有很大影响。