随机Burgers方程的有限体积方法∗

摘要

In this paper, we use the finite volume method to numerically solve the Burgers equation with uncertain input data. Firstly, an efficient numerical algorithm is proposed by using the second order finite difference in the time discretization and finite volume schemes in the spatial discretization, respectively. The main idea to use the different definition mode for nonlinear convection term. Secondly, when the boundary condition and the viscosity coefficient have a random perturbation, the stability and convergence of the new scheme are analyzed and verified. Finally, we make a conclusion that the influence of the stochastic disturbance on the boundary condition or viscosity coefficient in numerical calculation can be controlled by increasing the number of grid points.%　　本文应用有限体积方法研究带有不确定性输入参数的Burgers方程，其特点是在时间离散上采用二阶有限差分，在控制体上对非线性对流项采用不同的定义方式。在边界条件和粘性系数存在随机扰动的情况下，通过数值模拟验证了算法的收敛性和稳定性，并进一步测试了通过加密空间网格点的方法来抑制边界和粘性系数扰动对计算结果的影响。