Solving Navier–Stokes Equations with Stationary and Moving Interfaces on Unfitted Meshes
Solving Navier–Stokes Equations with Stationary and Moving Interfaces on Unfitted Meshes
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DOI：
10.1007/s10915-023-02414-z
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发表时间：
2023-12
影响因子：
2.5
通讯作者：
Yuan Chen;Xu Zhang
中科院分区：
文献类型：
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作者：
Yuan Chen;Xu Zhang
介绍了一种求解两相不可压Navier-Stokes方程的高精度浸入有限元方法。在空间离散中，我们使用新开发的浸没泰勒-胡德有限元。从理论上证明了新的IFE基函数的不均匀性。我们介绍了一种改进的部分惩罚IFE方法，它包括界面边缘和界面本身的惩罚。还为压力鲁棒性添加了重影惩罚。在时间离散中，采用了-格式和向后微分公式。采用牛顿法处理非线性平流。该方法在处理移动界面问题时完全避免了重新网格划分。由于我们的IFE空间与标准有限元空间的同构，新方法可以有效地更新全局矩阵，从而显着降低了整体计算成本。数值实验表明，该方法在静止界面和运动界面情况下，对速度均具有三阶收敛性，对压力均具有二阶收敛性。
This paper introduces a high-order immersed finite element (IFE) method to solve two-phase incompressible Navier–Stokes equations on interface-unfitted meshes. In spatial discretization, we use the newly developed immersed-Taylor-Hood finite element. The unisolvency of new IFE basis functions is theoretically established. We introduce an enhanced partially penalized IFE method which includes the penalization on both interface edges and the interface itself. Ghost penalties are also added for pressure robustness. In temporal discretization,-schemes and backward differentiation formulas are adopted. Newton’s method is used to handle the nonlinear advection. The proposed method completely circumvent re-meshing in tackling moving-interface problems. Thanks to the isomorphism of our IFE spaces with the standard finite element spaces, the new method enables efficient updates of global matrices, which significantly reduces the overall computational cost. Comprehensive numerical experiments show that the proposed method is third-order convergent for velocity and second-order for pressure in both stationary and moving interface cases.