Manifold method coupled velocity and pressure for Navier-Stokes equations and direct numerical solution of unsteady incompressible viscous flow
Manifold method coupled velocity and pressure for Navier-Stokes equations and direct numerical solution of unsteady incompressible viscous flow
复制标题
纳维-斯托克斯方程的速度和压力耦合流形方法以及非定常不可压缩粘性流的直接数值求解
DOI：
10.1016/j.compfluid.2010.04.005
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发表时间：
2010-09-01
影响因子：
2.8
通讯作者：
Yan, Jinhua
中科院分区：
文献类型：
--
作者：
Zhang, Zhengrong;Zhang, Xiangwei;Yan, Jinhua
讨论了数值流形方法(NMM)在非定常不可压缩粘性流纳维-斯托克斯(N-S)方程直接数值求解中的应用，并基于伽辽金加权残差法推导了N-S方程的数值流形格式。有限元覆盖系统采用速度线性多项式函数和压力常数函数的混合覆盖。补丁试验表明，混合覆盖流形单元满足稳定性条件，可直接求解速度和压力变量耦合的N-S方程。混合覆盖的数值格式也被证明是无条件稳定的。作为应用，混合盖四节点矩形流形单元被用来模拟典型驱动腔中的非定常不可压缩粘性流和水平通道中方形圆柱体周围的流动。从更少的计算变量和非常大的时间步长获得的高精度结果与参考文献中非常精细的单元网格和非常少的时间步长的紧凑有限差分解非常一致。数值试验表明，NMM是一种有效的、高阶精确的非定常不可压缩粘性流N-S方程数值方法。 (C) 2010 Elsevier Ltd. 保留所有权利。
Numerical manifold method (NMM) application to direct numerical solution for unsteady incompressible viscous flow Navier-Stokes (N-S) equations was discussed in this paper, and numerical manifold schemes for N-S equations were derived based on Galerkin weighted residuals method as well. Mixed covers with linear polynomial function for velocity and constant function for pressure was employed in finite element cover system. The patch test demonstrated that mixed covers manifold elements meet the stability conditions and can be applied to solve N-S equations coupled velocity and pressure variables directly. The numerical schemes with mixed covers have also been proved to be unconditionally stable. As applications, mixed cover 4-node rectangular manifold element has been used to simulate the unsteady incompressible viscous flow in typical driven cavity and flow around a square cylinder in a horizontal channel. High accurate results obtained from much less calculational variables and very large time steps are in very good agreement with the compact finite difference solutions from very fine element meshes and very less time steps in references. Numerical tests illustrate that NMM is an effective and high order accurate numerical method for unsteady incompressible viscous flow N-S equations. (C) 2010 Elsevier Ltd. All rights reserved.