SPECTRAL VISCOSITY METHOD WITH GENERALIZED HERMITE FUNCTIONS AND ITS SPECTRAL FILTER FOR NONLINEAR CONSERVATION LAWS
SPECTRAL VISCOSITY METHOD WITH GENERALIZED HERMITE FUNCTIONS AND ITS SPECTRAL FILTER FOR NONLINEAR CONSERVATION LAWS
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发表时间：
2014
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通讯作者：
Xue-ping Luo
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作者：
Xue-ping Luo
本文提出了一种新的谱粘性方法，用于求解非线性标量守恒律方程的全线解。所提出的方法是基于广义Hermite函数。严格证明了该方案收敛到唯一的熵解，通过使用补偿紧性参数。无粘Burger方程的数值实验支持了我们的结果。此外，我们进一步讨论了由我们的方法得到的近似解的后处理方法，以消除振荡远离间断。提出了一种新的由物理空间中的核函数定义的谱滤波器，并给出了远离不连续点的谱精度。
In this paper, we propose a new spectral viscosity method for the solution of nonlinear scalar conservation laws in the whole line. The proposed method is based on the generalized Hermite functions. It is shown rigorously that this scheme converges to the unique entropy solution by using compensated compactness arguments. The numerical experiments of the inviscid Burger’s equation support our result. Moreover, we step further to discuss the postprocessing method of the approximate solution obtained by our method to eliminate the oscillation away from the discontinuity. We suggest a new spectral filter defined by a kernel function in the physical space, and show the spectral accuracy at the points away from the discontinuity.