一维输运方程的编程求解及可视化

Programming Solution and Visualization of One-dimensional Transport Equation

输运方程是常见的数学物理方程之一,教材上通常采用的求解方法为分离数量法,此方法过程比较复杂,且适用条件苛刻,不适用于一般的输运方程,因此学生学习起来比较困难。本文采用有限差分方法求解一维输运方程的数值解并进行可视化,可使同学们直观地理解初始条件和边界对函数值的影响。

The transport equation is one of the common mathematical and physical equations.The solution method usually used in the textbook is the separated quantity method.The process of this method is more complicated and the conditions are harsh.It is not suitable for the general transport equation,so it is difficult for students to learn.In this paper,the finite difference method is used to solve the numerical solution of the one-dimensional transport equation and visualize it,so that students can intuitively understand the influence of initial conditions and boundaries on the function value.