论文标题
稳定的公式，用于频域中不稳定的不稳定Stokes方程的溶液
A stabilized formulation for the solution of the incompressible unsteady Stokes equations in the frequency domain
论文作者
论文摘要
引入了一种稳定的有限元方法，以模拟时间周期性的蠕变流，例如在心肺系统中发现的流量。新技术以频率而不是时域配制，严格使用真实算术，并允许使用相似的形状函数用于压力和速度，以易于实现。它涉及将压力的拉普拉斯添加到连续性方程中，具有复杂值稳定参数，该参数是从动量方程式系统地衍生而来的。数值实验表明，在各种条件下，在复杂和规范的几何形状中模拟流中所提出的方法的出色精度和鲁棒性。目前的方法在计算成本和可扩展性方面显着优于传统求解器，这将整体解决方案转换时间降低了几个数量级。
A stabilized finite element method is introduced for the simulation of time-periodic creeping flows, such as those found in the cardiorespiratory systems. The new technique, which is formulated in the frequency rather than time domain, strictly uses real arithmetics and permits the use of similar shape functions for pressure and velocity for ease of implementation. It involves the addition of the Laplacian of pressure to the continuity equation with a complex-valued stabilization parameter that is derived systematically from the momentum equation. The numerical experiments show the excellent accuracy and robustness of the proposed method in simulating flows in complex and canonical geometries for a wide range of conditions. The present method significantly outperforms a traditional solver in terms of both computational cost and scalability, which lowers the overall solution turnover time by several orders of magnitude.
