三维采空区内瓦斯、氮气的扩散运动及有限元解法

DIFFUSION OF METHANE AND NITROGEN IN 3D GOAF AND THE FINITE ELEMENT SOLUTION

应用三维多孔介质流场的紊流扩散方程和迎风加权Ｇａｌｅｒｋｉｎ有限元法，研究瓦斯、氮气在三维采空区内的扩散运动和浓度分布．给出的结点加权法有效地避免了求解扩散方程时的数值振荡．简单介绍了三维采空区速度场的解法，此速度场是按照采空区非线性渗流实际特点，依据与三维多孔介质流场紊流扩散方程相匹配的非线性渗流方程，应用文中提出的非线性渗流的Ｈ－Ｖ方程组和有限元法得出的．最后，给出了一个三维采空区注氮问题的典型算例．

The diffusion and distribution of methane and nitrogen concentration in a 3D goaf was studied by applying the turbulent diffusion equation to the 3D porous medium fluid field and the upwind finite element method. The method of node weighting given in the paper can avoid effectively oscillation of the values when the diffusion equation is solved. The method for solving the velocity field in 3D goaf is briefly described. The velocity field is obtained by using H V equation and FEM compatible with the turbulent diffusion equation of a 3D porous medium fluid field based on the non linear infiltration characteristics in the goaf. Finally, a typical example of injecting nitrogen in the 3D goaf is described.