二维稳态对流扩散问题的直接边界元方法

讨论了基于指数变量变换的二维稳态对流扩散方程的直接边界元解法,把对流扩散方程转化为与之等价的修正Helmholtz方程,利用其基本解和Green公式得到相应的直接边界积分方程和解的积分表达式.然后,通过逆变换推导出对流扩散方程的直接边界积分方程和解的积分表达式,并采用常单元来离散边界积分方程,完成对流扩散方程的求解.最后,通过数值算例验证方法的有效性.

A Direct Boundary Element Methods for Two Dimensional Steady-State Convection-Diffusion Problems

A direct boundary element methods based on exponential variable transformation for solving two-dimensional steady-state convection-diffusion problems is described in this paper first.Second,use of the exponential variable transformation,the convection-diffusion equation is converted into a modified Helmholz equation.The fundamental solution of Helmholz equation and Green formula were used to obtain the direct boundary integral equation.And then,the direct boundary integral equation of convection-diffusion was obtained by using inverse transformation,which is a discrete by using constant elements. Finally,the whole course of solving convection-diffusion is completed and validity of the methods is discussed by test example.