地球科學中的一類耦合拋物方程組的數(shù)值模擬.pdf

1、地質(zhì)流體的性質(zhì)和動力學行為是當前地球科學研究的前沿領域.銅陵冬瓜山層控夕卡巖型銅礦床成礦作用中礦質(zhì)輸運-化學反應耦合過程其動力學數(shù)學模型是一個耦合拋物型偏微分方程組： ()(-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,

2、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＜∞.本文用降階法對這一數(shù)學模型建立了一個二階差分格式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

3、/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'/r'2/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+ηjδzc

4、k-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≤

5、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.在每一時間層上只需解若干個三對角線性方程組，可用追趕法求解.用能量分析法給出了差分解的先驗估計式，證明了差分格式的唯一可解性、無條件穩(wěn)定性和收斂性，在L2范數(shù)下收斂階為O(τ2+h2+(-h)2).最后給出