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Integrated radial basis functions (IRBFs) to simulate nonlinear advection–diffusion equations with smooth and non-smooth initial data
Engineering with Computers ( IF 8.7 ) Pub Date : 2020-07-06 , DOI: 10.1007/s00366-020-01039-2
Ali Ebrahimijahan , Mehdi Dehghan , Mostafa Abbaszadeh

In this article, a meshfree method for the numerical solution of conversation law equations is considered. Some problems which have shock such as advection problems are not properly solved by radial basis function collocation meshfree method. Therefore, we use the integrated radial basis function (IRBF) method for some of these problems. In the current study, the governing models have been discretized by IRBF technique in the spatial direction and by finite difference approximation for time variable. This converts the main problem to a system of nonlinear ordinary differential equations (ODEs). Furthermore, the obtained ODEs will be solved by Runge–Kutta technique. This is the meshless method of lines technique. Numerical examples indicate the acceptable accuracy, proficiency and easy implementation of the presented method.

中文翻译:

集成径向基函数 (IRBF) 可使用平滑和非平滑初始数据模拟非线性对流-扩散方程

在本文中,考虑了会话律方程数值解的无网格方法。径向基函数搭配无网格方法不能很好地解决一些有冲击的问题,如平流问题。因此,我们对其中一些问题使用集成径向基函数 (IRBF) 方法。在目前的研究中,控制模型已通过空间方向的 IRBF 技术和时间变量的有限差分近似进行离散化。这将主要问题转换为非线性常微分方程 (ODE) 系统。此外,获得的 ODE 将通过 Runge-Kutta 技术求解。这是线条技术的无网格方法。数值例子表明所提出的方法的可接受的准确性、熟练度和容易实施。
更新日期:2020-07-06
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