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首页> 外文期刊>Engineering analysis with boundary elements >Two-dimensional simulation of the damped Kuramoto-Sivashinsky equation via radial basis function-generated finite difference scheme combined with an exponential time discretization
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Two-dimensional simulation of the damped Kuramoto-Sivashinsky equation via radial basis function-generated finite difference scheme combined with an exponential time discretization

机译：阻尼Kuramoto-Sivashinsky方程的二维模拟，采用径向基函数生成的有限差分格式并结合指数时间离散化

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摘要

We apply a numerical scheme based on a meshless method in space and an explicit exponential Runge-Kutta in time for the solution of the damped Kuramoto-Sivashinsky equation in two-dimensional spaces. The proposed meshless method is radial basis function-generated finite difference, which approximates the derivatives of the unknown function with respect to the spatial variables by a linear combination of the function values at given points in the domain and weights. Also, in this approach there is no need a mesh or triangulation for approximation. For each point, the weights are computed separately in its local sub-domain by solving a small radial basis function interpolant. Besides, a numerical algorithm based on singular value decomposition of the local radial basis function interpolation matrix [59] is applied to find the suitable shape parameter for each interpolation problem. We also consider an explicit time discretization based on exponential Runge-Kutta scheme such that its stability region is bigger than the classical form of Runge-Kutta method. Some numerical simulations are provided on the square, circular and annular domains to show the capability of the numerical scheme proposed here.
机译：我们在空间中应用了基于无网格方法的数值方案，并在时间上应用了显式指数Runge-Kutta来求解二维空间中的阻尼Kuramoto-Sivashinsky方程。提出的无网格方法是径向基函数生成的有限差分，它通过域和权重的给定点处函数值的线性组合来近似未知函数相对于空间变量的导数。同样，在这种方法中，不需要网格或三角剖分进行逼近。对于每个点，通过求解较小的径向基函数插值，分别在其局部子域中计算权重。此外，基于局部径向基函数插值矩阵[59]的奇异值分解的数值算法被应用于为每个插值问题找到合适的形状参数。我们还考虑了基于指数Runge-Kutta方案的显式时间离散化，使得其稳定区域大于Runge-Kutta方法的经典形式。在正方形，圆形和环形域上提供了一些数值模拟，以显示此处提出的数值方案的能力。

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