一种新的混合有限体积元法求解一维多孔介质问题

针对一维多孔介质问题用标准混合有限体积元法求解时会出现数值解波阵面不能向前传播的现象, 提出一种新的混合有限体积元法求解退化问题, 其中流变量仅包含原始变量对空间变量的导数. 结果表明, 该方法可避免数值解波阵面不能向前传播的现象, 并能很好地捕捉数值解界面. 数值实验验证了该方法的有效性.

A New Mixed Finite Volume Element Method for SolvingOne-Dimensional Porous Medium Problems

For the one dimensional porous medium problem, wave front of the numerical solution could not propagate forward when  the standard mixed finite volume element method was used to solve them, we proposed  a new mixed finite volume element method for  solving the degradation problem, in which the  flux variable only included the derivative of the original variable  to spacial variable. The results show that the  method can avoid the phenomenon that wave front of the numerical solution can  not propagate forward, and can capture the interface of numerical solution well. The validity of the  method is verified by numerical experiments.