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地质流体的性质和动力学行为是当前地球科学研究的前沿领域.铜陵冬瓜山层控夕卡岩型铜矿床成矿作用中矿质输运-化学反应耦合过程其动力学数学模型是一个耦合抛物型偏微分方程组：
()(-C)/()t-d/r()2(-)C/()x2+λ(-C)=0,b＜x＜B,0＜z＜∞,0＜t≤T,()C/()t+v/r()C/()z-d/r()2C/()z2+λC-φd/br()(-C)/()x|x=b=0,0＜z＜∞,0＜t≤T,(-C)(x,z,0)=0,b≤x≤B,0≤z＜∞,(-C)(b,z,t)=C(z,t),0≤z＜∞,0＜t≤T,()(-C)/()x(B,z,t)=0，0≤z＜∞,0＜t≤T,C(0,t)=C0,C(∞,t)=0,0＜t≤T,C(z,0)=0,0≤z＜∞.本文用降阶法对这一数学模型建立了一个二阶差分格式1/2(δt(-c)k-1/2i-1/2,j-1/2+δt(-c)k-1/2i+1/2,j-1/2)-d/r(δ2x(-c)k-1/2i,j-1/2)+λ/2((-c)k-1/2i-1/2,j-1/2+(-c)k-1/2i+1/2,j-1/2)=0,1≤i≤M-1,1≤j≤N,1≤k≤K,δt(-c)k-1/2M-1/2,j-1/2+d/r2/hδx(-c)k-1/2M-1/2,j-1/2+λ(-c)k-1/2M-1/2,j-1/2=0,1≤j≤N,1≤k≤K,ξjδtck-1/2j-1/2+ηjδtck-1/2j+1/2+v/r(ξjδzck-1/2j-1/2+ηjδzck-1/2j+1/2)-d/rδ2zck-1/2j+λ(ξjck-1/2j-1/2+ηjck-1/2j+1/2)-φd/br{ξj[δx(-c)k-1/21/2,j-1/2-hr/2d(δt(-c)k-1/21/2,j-1/2+λ(-c)k-1/21/2,j-1/2)]+ηj[δx(-ck-1/21/2,j+1/2-hr/2d(δt(-c)k-1/21/2,j+1/2+λ(-c)k-1/21/2,j+1/2)]}=0,1≤j≤N-1,1≤k≤K,(-c)0i,j-1/2=0,0≤i≤M,1≤j≤N,(-c)k-1/20,j-1/2=ck-1/2j-1/2,1≤j≤N,1≤k≤K,ck-1/20=C0，ck-1/2N=0，1≤k≤K,c0j=0,0≤j≤N.在每一时间层上只需解若干个三对角线性方程组，可用追赶法求解.用能量分析法给出了差分解的先验估计式，证明了差分格式的唯一可解性、无条件稳定性和收敛性，在L2范数下收敛阶为O(τ2+h2+(-h)2).最后给出的数值例子验证了理论分析结果.