基于通量限制器的时间分数阶Burgers方程数值解法

Numerical Solution of Time-Fractional Burgers Equation Based on Flux Limiter

摘要: 对于求解可能具有激波等不连续点的时间分数阶守恒律，当分数阶γ接近于0时，目前还没有有效的方法求解时间分数阶非线性离散系统，本文以时间分数阶Burgers方程为例，运用多重网格迭代方法进行求解，对于对流项，采用通量限制器，使得新的数值通量在光滑区域变为高阶通量而在间断附近变为低阶通量，从而使问题的解达到更高阶精度，并在不同的γ取值以及不同的初边值条件下进行了有效的数值实验。

Abstract: For solving the fractional time conservation law that may have discontinuities such as shock waves, when the fractional order γ is close to 0, there is no effective method to solve the fractional nonline-ar discrete system. Taking the time fractional Burgers equation as an example, this paper applies the multi-grid iterative method to solve the problem. For the convection term, a flux limiter is adopted to make the new numerical flux become a higher order flux in the smooth area and a lower order flux near the discontinuity, thus achieving a higher order precision. The effective numerical experiments are carried out with different values of γ and different initial boundary values.