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Application of a local meshless modified characteristic method to incompressible fluid flows with heat transport problem
Engineering Analysis With Boundary Elements ( IF 4.2 ) Pub Date : 2021-11-18 , DOI: 10.1016/j.enganabound.2021.09.033
Zineb Tabbakh 1 , Rachid Ellaia 1 , Driss Ouazar 2
Affiliation  

Radial basis function (RBF) has been accurately used for the spatial discretization to solve PDE problems. In this paper, a practical stabilization of the local formulation of the radial basis function (RBF) method is presented to solve the incompressible fluid flows with heat transport problems. To avoid the nonlinearity of the convective term, we include the modified method of characteristics to construct stable and efficient methods. The governing equations are the incompressible Navier–Stokes equations/Boussinesq approximation coupled with the heat transport equation. The spatial discretization carried out using the local radial basis function (LRBF) method on a uniform and non-uniform nodes distribution in a complex domain. The proposed method can be described as a fractional step splitting where the convective and generalized Stokes parts are treated separately. To solve the generalized Stokes problem, we used a projection/fractional step method that requires velocity–pressure decoupling. The proposed approach’s performance is tested on three benchmark problems and natural convection flow in a regular and irregular domains. We compare the results with different numerical solutions published in the literature. The obtained numerical results demonstrate the accuracy and stability of the proposed meshless method.



中文翻译:

局部无网格修正特征法在具有传热问题的不可压缩流体流动中的应用

径向基函数 (RBF) 已被准确地用于空间离散化以解决 PDE 问题。在本文中,提出了径向基函数 (RBF) 方法局部公式的实际稳定性,以解决具有热传输问题的不可压缩流体流动。为了避免对流项的非线性,我们引入了改进的特征方法来构建稳定有效的方法。控制方程是不可压缩的 Navier-Stokes 方程/Boussinesq 近似与热传输方程相结合。使用局部径向基函数 (LRBF) 方法对复杂域中的均匀和非均匀节点分布进行空间离散化。所提出的方法可以描述为分步分裂,其中对流部分和广义斯托克斯部分被分开处理。为了解决广义斯托克斯问题,我们使用了需要速度-压力解耦的投影/分数阶跃方法。所提出的方法的性能在规则和不规则域中的三个基准问题和自然对流流上进行了测试。我们将结果与文献中发表的不同数值解进行比较。获得的数值结果证明了所提出的无网格方法的准确性和稳定性。所提出的方法的性能在规则和不规则域中的三个基准问题和自然对流流上进行了测试。我们将结果与文献中发表的不同数值解进行比较。获得的数值结果证明了所提出的无网格方法的准确性和稳定性。所提出的方法的性能在规则和不规则域中的三个基准问题和自然对流流上进行了测试。我们将结果与文献中发表的不同数值解进行比较。获得的数值结果证明了所提出的无网格方法的准确性和稳定性。

更新日期:2021-11-19
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