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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >Global matrix-free finite-element scheme for natural convection in a square cavity with step blockage
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Global matrix-free finite-element scheme for natural convection in a square cavity with step blockage

机译：具有阶梯阻塞的方腔内自然对流的全局无矩阵有限元方案

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摘要

A global matrix-free finite-element scheme is proposed for the solution of two-dimensional Navier-Stokes equations in velocity-vorticity form. By including the boundary conditions of the field variables at the element level itself, the global assembly of matrices is completely eliminated, thus resulting in a significant saving in computer memory. Only the global vectors obtained as a result of matrix-vector products are assembled at the time of solution of the simultaneous equations, using a conjugate gradient iterative solver. The method is validated by solving a benchmark problem on natural convection in a square cavity. The incompressibility constraint of the flow field is satisfied by imposing the vorticity definition at the boundaries using a second-order-accurate Taylor series expansion scheme.
机译：针对二维涡旋形式的Navier-Stokes方程，提出了一种全局无矩阵有限元格式。通过在元素级别本身包括字段变量的边界条件，可以完全消除矩阵的全局组装，从而显着节省了计算机内存。使用共轭梯度迭代求解器，在求解联立方程时，仅组装由于矩阵向量乘积而获得的整体向量。通过解决方腔内自然对流的基准问题验证了该方法的有效性。通过使用二阶精确泰勒级数展开方案在边界处强加涡度定义，可以满足流场的不可压缩性约束。

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