瞬态对流-扩散方程的变分多尺度解法

Variational multiscale method for the transient convection-diffusion equations

根据变分多尺度思想,求解了瞬态线性和非线性对流-扩散方程。文中为了简化"细"尺度方程的求解,忽略了该方程的瞬态性,分别用高阶多项式泡函数(High-order Polynomial Bubble)和自由残量泡(Residual Free Bubble)函数近似"细"尺度解,进而引入了消除数值伪振荡的稳定化结构。数值算例验证了本文方法的精确性、稳定性和对高Peclet数问题的适应性,证明了上述对"细"尺度模型的简化是可行的。

This paper followed the lines of variational multi-scale method and presented a variational multi-scale finite element method for the transient linear and nonlinear convection-diffusion equations.The θ family of methods were employed for the time discretization.Making a proper approximation to the fine scale solution,variational multi-scale method can stabilize the linear and nonlinear convective term with the help of the stabilization term based on the residual of the Partial Differential Equations.Modeling the fine scale by high-order polynomial bubble and residual free bubble,with the assumption that the fine scale solution is time independent corrects the lack of stability of the standard Galerkin weak form.The numerical results show that the method is stable,accurate,and yields high approximation to the high Peclet number problems.