h‐adaptive finite element solution of high Rayleigh number thermally driven cavity problem
h‐adaptive finite element solution of high Rayleigh number thermally driven cavity problem
复制标题
DOI：
10.1108/09615530010347187
复制
发表时间：
2000-09
影响因子：
4.2
通讯作者：
David A. Mayne;A. Usmani;M. Crapper
中科院分区：
文献类型：
--
作者：
David A. Mayne;A. Usmani;M. Crapper
一个求解耦合Navier-Stokes方程和能量方程的h-自适应有限元程序被用来求解热驱动空腔问题。浮力用Boussinesq近似表示。该问题的特征在于在高瑞利数（>106）下的非常薄的边界层。然而，稳态的解决方案是可以实现的充分的离散化。这就是自适应有限元方法提供了一种强大的方法来实现最佳解决方案，而不必预先定义网格，这可能是不够的或太昂贵。稳态和瞬态结果给出了六个不同的瑞利数在103至108的范围内的普朗特数为0.71。基于后验误差估计的h-自适应的使用被发现以合理的计算成本确保非常准确的问题解决方案。
An h‐adaptive finite element code for solving coupled Navier‐Stokes and energy equations is used to solve the thermally driven cavity problem. The buoyancy forces are represented using the Boussinesq approximation. The problem is characterised by very thin boundary layers at high values of Rayleigh number (>106). However, steady state solutions are achievable with adequate discretisation. This is where the auto‐adaptive finite element method provides a powerful means of achieving optimal solutions without having to pre‐define a mesh, which may be either inadequate or too expensive. Steady state and transient results are given for six different Rayleigh numbers in the range 103 to 108 for a Prandtl number of 0.71. The use of h‐adaptivity, based on a posteriori error estimation, is found to ensure a very accurate problem solution at a reasonable computational cost.