论文标题
变化可变和不连续性捕获的对流反应方程的有限元公式
Finite-Element Formulation for Advection-Reaction Equations with Change of Variable and Discontinuity Capturing
论文作者
论文摘要
我们建议更改可变方法和不连续性捕获方法，以确保通过有限元方法离散的对流反应方程的物理约束。可变的这种变化将浓度限制在上界下方的浓度以非常自然的方式限制。对于非阴性约束，我们建议使用在参考元素上定义的不连续性捕获方法，该方法与各向异性交叉驱动器结合使用。这种不连续性捕获不能完全消除负值，但有效地最大程度地减少了它们的发生。所提出的方法应用于不同的生物物理模型，并与FDA基准血液泵的实验结果显示出良好的一致性，用于生理红细胞孔的形成模型。
We propose a change of variable approach and discontinuity capturing methods to ensure physical constraints for advection-reaction equations discretized by the finite element method. This change of variable confines the concentration below an upper bound in a very natural way. For the non-negativity constraint, we propose to use a discontinuity capturing method defined on the reference element that is combined with an anisotropic crosswind-dissipation operator. This discontinuity capturing cannot completely eliminate negative values but effectively minimizes their occurrence. The proposed methods are applied to different biophysical models and show a good agreement with experimental results for the FDA benchmark blood pump for a physiological red blood cell pore formation model.
