重心Lagrange插值配点法求解气动力学方程

Barycentric Lagrange Interpolation Collocation Method for Solving Gas Dynamics Equations

为了使得数值解更加准确,本文使用了重心Lagrange插值配点法来求解气动力学方程.对空间域和时间域的变量均采用切比雪夫节点离散,方程的未知函数及其偏导数采用插值函数和微分矩阵进行离散,初边值条件采用置换法进行施加,然后进行求解.此外,为了说明该方法的可靠性和有效性,本文求解了三个数值算例,同时比较了不同插值节点下三种误差值的变化.数值解和解析解图像的高度吻合表明了重心Lagrange插值配点法的实用性和有效性.

In this paper,in order to obtain the high-precision numerical solutions,the barycentric Lagrange interpolation collocation method is used to solve the gas dynamics equations.The variables in the space domain and the time domain are all discretized by using Chebyshev nodes.The unknown function and its partial derivative of the equations are discretized by interpolation function and differential matrix.The initial and boundary conditions are applied by the substitution method to obtain the solutions.In addition,in order to illustrate the reliability and effectiveness of the method,three numerical examples of the gas dynamics equations are solved and the significant variations of three error values are compared.High agreement between numerical and analytical solution images can show the high accuracy and effectiveness of the barycentric Lagrange interpolation collocation method.