求解对流——扩散方程的边界元与特征线混合法

A Boundary Element-Characteristic Curve Method for Solving Diffusion-Convective Equation

作者根据对流——扩散方程的数学物理特性,应用算子分裂原理,把对流——扩散算子分裂成为Lagrange形式下的对流算子和Euler形式下的纯扩散算子,并分别采用完全特征线法和边界元法计算由对流作用引起的溶质迁移扩散和由浓度梯度产生的纯扩散。数值试验表明,该方法能方便地把分裂格式很好地耦合起来,具有计算速度快、精度高等优点,并在各种Peclet条件数下均可获得足够精度的数值解。

A Boundary element-characteristic curve method for solving diffusion-convectie equation numerically has been presented in this paper. Depend on operator splitting technique, the equation is divided into diffusion operator and convective operator in every small time intcral △t(△t= t/n). The convective problem is calculated along the characteristic curve in a Lagrangian scheme and the diffusion problem is solved by using boundary element method in a Eulerian mesh. For the diffusion-convective equation with the initial and doundary conditions numerical solution can be obtained by repeating the same integrations n times. Two typical examples bare been calculated in order to verify the correctitudc of this method. The calculating results have shown that the agreement between the numerical solutions and the exact solutions is quite satisfactory under various Peclet number conditions. This method can easily couple the diffusion operator in Eulerian coodinate mesh and the convective operator in Lagrange scheme, so it can eliminate the numerical errors due to the interpolate in the nodes. It can be also extended to solve two or three dimensional diffusion-convective problems.