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Multiquadric RBF-FD method for the convection-dominated diffusion problems base on Shishkin nodes

机译:基于Shishkin节点的对流主导扩散问题的多二次RBF-FD方法

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摘要

In this paper, a new hybrid scheme based multiquadric radial basis function-generated finite difference (RBF-FD) method with Shishkin nodes is proposed to solve stationary convection-dominated diffusion problems, i.e., the boundary layer problems, which combines the midpoint upwind scheme on the coarse grid with a standard central scheme on the fine grid. Numerical results demonstrate the hybrid scheme with Shishkin nodes has an absolute advantage in accurate over standard upwind scheme with equidistant nodes. Moreover, by varying the shape parameter in multiquadric RBF-FD method, the convergence rates of numerical solutions have been further improved compared with the corresponding FD method.
机译:提出了一种新的混合方案,基于Shishkin节点的多二次径向基函数生成有限差分(RBF-FD)方法,结合中点迎风方案解决了平稳对流占主导的扩散问题,即边界层问题。在粗网格上使用标准中心方案在细网格上。数值结果表明,具有Shishkin节点的混合方案在精度上优于具有等距节点的标准迎风方案。此外,通过改变多二次RBF-FD方法中的形状参数,与相应的FD方法相比,数值解的收敛速度得到了进一步提高。

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