A numerical method for solving the 3D unsteady incompressible Navier-Stokes equations in curvilinear domains with complex immersed boundaries
A numerical method for solving the 3D unsteady incompressible Navier-Stokes equations in curvilinear domains with complex immersed boundaries
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DOI：
10.1016/j.jcp.2007.02.017
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发表时间：
2007-08-10
影响因子：
4.1
通讯作者：
Sotiropoulos, Fotis
中科院分区：
文献类型：
--
作者：
Ge, Liang;Sotiropoulos, Fotis
本文提出了一种新的数值方法，它将边界协调网格与一个尖锐的界面结合起来，即浸入边界法。该方法旨在模拟包含复杂的内部流动，移动浸没边界，如在几个心血管应用中遇到的。背景域（例如空主动脉）用曲线边界拟合网格有效地离散化，而复杂的移动浸没边界（例如人工心脏瓣膜）用Gilmanov和Sotiropoulos的尖锐界面、混合笛卡尔/浸没边界方法处理[A. Gilmanov，F. Sotiropoulos，A hybrid carriage/immersive boundary method for simulating flows with 3d，geometrically complex，moving bodies，Journal of Computational Physics 207（2005）457-492.].为了便于在复杂流动模拟中实现这种新的建模范式，开发了一种精确有效的数值方法来求解广义曲线坐标系下的非定常不可压缩Navier-Stokes方程。该方法采用了一种新的，全曲线交错网格离散化方法，它不需要显式评估的Christoffel符号或离散化的所有三个动量方程在细胞接口在以前的配方。该方程集成的时间使用一个有效的，二阶精度的分步方法加上一个雅可比自由，牛顿-克雷洛夫求解器的动量方程和GMRES求解器增强与多重网格作为预条件的泊松方程。在精细计算网格上进行了几个数值实验，以证明所提出的方法对标准基准问题以及通过弯曲管道弯曲的非定常脉动流的准确性和效率。为了证明该方法模拟复杂流动的能力，移动浸没边界，我们将其应用于计算通过机械双叶心脏瓣膜的脉动生理流量，该瓣膜安装在具有解剖学样三窦的模型直主动脉中。(c)2007年爱思唯尔公司All rights reserved.
A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus. (c) 2007 Elsevier Inc. All rights reserved.