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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A fictitious domain/distributed Lagrange multiplier based fluid-structure interaction scheme with hierarchical B-Spline grids
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A fictitious domain/distributed Lagrange multiplier based fluid-structure interaction scheme with hierarchical B-Spline grids

机译：基于虚拟域/分布式拉格朗日乘子的流体-结构相互作用方案，带有分层B样条网格

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摘要

We present a numerical scheme for fluid-structure interaction based on hierarchical B-Spline grids and fictitious domain/distributed Lagrange multipliers. The incompressible Navier-Stokes equations are solved over a Cartesian grid discretised with B-Splines. The fluid grid near the immersed solids is refined locally using hierarchical B-Splines. The immersed solid is modelled as geometrically-exact beam discretised with standard linear Lagrange shape functions. The kinematic constraint at the fluid-solid interface is enforced with distributed Lagrange multipliers. The unconditionally-stable and second-order accurate generalised-a method is used for integration in time for both the fluid and solid domains. A fully-implicit and fully-coupled solution scheme is developed by using the Newton-Raphson method to solve the non-linear system of equations obtained with Galerkin weak formulation. First, the spatial and temporal convergence of the proposed scheme is assessed by studying steady and unsteady flow past a fixed cylinder. Then, the scheme is applied to several benchmark problems to demonstrate the efficiency and robustness of the proposed scheme. The results obtained with the present scheme are compared with the reference values. (C) 2015 Elsevier B.V. All rights reserved.
机译：我们提出了一种基于层次B样条网格和虚拟域/分布式拉格朗日乘子的流体-结构相互作用的数值方案。不可压缩的Navier-Stokes方程是在用B样条离散的笛卡尔网格上求解的。使用层次化B样条曲线可以局部优化浸没固体附近的流体网格。将浸没的实体建模为使用标准线性Lagrange形状函数离散化的精确几何束。流体-固体界面的运动学约束是通过分布式拉格朗日乘数来实现的。使用无条件稳定和二阶精确广义方法对流域和固体域进行时间积分。通过使用牛顿-拉夫森方法，开发了一种完全隐式和完全耦合的求解方案，以解决用Galerkin弱公式获得的非线性方程组。首先，通过研究流经固定圆柱体的稳态和非稳态流来评估所提出方案的时空收敛性。然后，将该方案应用于几个基准问题，以证明所提出方案的效率和鲁棒性。将本方案获得的结果与参考值进行比较。 （C）2015 Elsevier B.V.保留所有权利。

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