CAJ | 학술논문

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.
본문응용유한체적방법연구대유불학정성수입삼수적Burgers방정,기특점시재시간리산상채용이계유한차분,재공제체상대비선성대류항채용불동적정의방식.재변계조건화점성계수존재수궤우동적정황하,통과수치모의험증료산법적수렴성화은정성,병진일보측시료통과가밀공간망격점적방법래억제변계화점성계수우동대계산결과적영향.
In this paper, we use the finite volume method to numerically solve the Burgers equation with uncertain input data. Firstly, an e?cient 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 coe?cient 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 coe?cient in numerical calculation can be controlled by increasing the number of grid points.