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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations
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Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations

机译：基于局部径向基函数的微分求积方法及其在求解二维不可压缩Navier-Stokes方程中的应用

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Local radial basis function-based differential quadrature method is presented in detail in this paper. The method is a natural mesh-free approach. Like the conventional differential quadrature (DQ) method, it discretizes any derivative at a knot by a weighted linear sum of functional values at its neighbouring knots, which may be distributed randomly. However, different from the conventional DQ method, the weighting coefficients in present method are determined by taking the radial basis functions (RBFs) instead of high order polynomials as the test functions. The method works in a similar fashion as conventional finite difference schemes but with "truly" mesh-free property. In this paper, we mainly concentrate on the multiquadric RBFs since they have exponential convergence. The effects of shape parameter c on the accuracy of numerical solution of linear and nonlinear partial differential equations are studied, and how the value of optimal c varies with the number of local support knots is also numerically demonstrated. The proposed method is validated by its application to the simulation of natural convection in a square cavity. Excellent numerical results are obtained on an irregular knot distribution.
机译：详细介绍了基于局部径向基函数的微分求积方法。该方法是自然的无网格方法。像传统的差分正交（DQ）方法一样，它通过其相邻结处的函数值的加权线性总和来离散结处的任何导数，这些函数值可以随机分布。然而，与传统的DQ方法不同，本方法中的加权系数是通过采用径向基函数（RBF）而不是高阶多项式作为测试函数来确定的。该方法以与常规有限差分方案相似的方式工作，但具有“真正”的无网格特性。在本文中，我们主要关注多二次RBF，因为它们具有指数收敛性。研究了形状参数c对线性和非线性偏微分方程数值解精度的影响，并数值模拟了最佳c值如何随局部支撑结数的变化而变化。该方法在方腔自然对流模拟中的应用得到了验证。在不规则结分布上可获得出色的数值结果。

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