层流不可压缩Navier-Stokes方程精确的无迭代混合稳定化格式：在流固耦合中的应用
Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier-Stokes: Applications to fluid-structure interaction
摘要：
稳定化混合速度-压力列式是计算层流不可压Navier-Stokes方程数值解的常用有限元格式之一。在这些公式中，Newton-Raphson格式被用来解决对流项中的非线性。这种方法的一个基本问题是在每个负载/时间步长的Newton-Raphson迭代中产生的计算成本。在本文中，我们提出了一个迭代自由混合有限元制定不可压缩Navier-Stokes方程，保持二阶时间精度的广义α和相关计划的速度和压力场。首先，我们证明了二阶时间精度使用数值收敛研究的一个例子与制造的解决方案。随后，我们通过研究流过固定圆柱体的基准示例来评估所提出的方案的精度和计算效益。为了在更广泛的背景下展示所提出的技术的适用性，还考虑了用于没有稳定化的制剂的inf-sup稳定P2-P1对。最后，所产生的好处，使用所提出的方案的流体-结构相互作用问题的说明使用两个基准的例子在流体-柔性结构相互作用。
英文摘要：
Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to solve the nonlinearity in the convection term. One fundamental issue with this approach is the computational cost incurred in the Newton-Raphson iterations at every load/time step. In this paper, we present an iteration-free mixed finite element formulation for incompressible Navier-Stokes that preserves second-order temporal accuracy of the generalised-alpha and related schemes for both velocity and pressure fields. First, we demonstrate the second-order temporal accuracy using numerical convergence studies for an example with a manufactured solution. Later, we assess the accuracy and the computational benefits of the proposed scheme by studying the benchmark example of flow past a fixed circular cylinder. Towards showcasing the applicability of the proposed technique in a wider context, the inf-sup stable P2-P1 pair for the formulation without stabilisation is also considered. Finally, the resulting benefits of using the proposed scheme for fluid-structure interaction problems is illustrated using two benchmark examples in fluid-flexible structure interaction.
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