Entropy stable essentially nonoscillatory methods based on RBF reconstruction
Entropy stable essentially nonoscillatory methods based on RBF reconstruction
复制标题
基于 RBF 重建的熵稳定本质上非振荡方法
DOI：
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发表时间：
2018
期刊：
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通讯作者：
Fabian Mönkeberg
中科院分区：
文献类型：
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作者：
J. Hesthaven;Fabian Mönkeberg
为了求解双曲守恒律，我们提出了基于径向基函数的高阶本质非振荡方法。介绍了一维问题的熵稳定任意高阶有限差分法（RBF-TeCNOp）和熵稳定二阶有限体积法（RBF-EFV2）。因此，我们证明了基于径向基函数的方法与基于多项式重构的方法一样强大。主要贡献是构造了一种算法和一个平滑指示器，以确保在一般一维网格上插值函数满足符号性质。
To solve hyperbolic conservation laws we propose to use high-order essentially nonoscillatory methods based on radial basis functions. We introduce an entropy stable arbitrary high-order finite difference method (RBF-TeCNOp) and an entropy stable second order finite volume method (RBF-EFV2) for one-dimensional problems. Thus, we show that methods based on radial basis functions are as powerful as methods based on polynomial reconstruction. The main contribution is the construction of an algorithm and a smoothness indicator that ensures an interpolation function which fulfills the sign-property on general one dimensional grids.