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Guangli March 25, 2006 22:12

Can someone tell me how to solve this equation!

Hello everyone ,i'm a beginner of numerical simulation, and i met a problem, can someone help me ,many thanks.

I want to solve the equation div(f(s)grad(s))=R(x,y) for 2D,where f(s)is highly relative with S,if i solve it as follows: assuming S-----calculate f(s)-------solve the equation-----update f(s)------solve the equation-----....... It seems the result is not reasonable,can someone help me for other methods,thanks! sincerely Guangli

Chin Fook March 28, 2006 23:50

Re: Can someone tell me how to solve this equation
f(s) is a function of a function. It can be a nonlinear term with F(s)Grad(s). Where can you find those application? R(x,y) is probably the source term or forcing function.

Guangli March 29, 2006 00:51

Re: Can someone tell me how to solve this equation
Thanks,actually,the original form of the equation is Div(F1(s)grad(F2(s))=R(x,y),and R(x,y)is the source term,the equation is deduced as follows: for two phase flow in poroous media,the relationship between gas pressure and the liquid pressure and the capillary pressure are: Pc=pg-pl; for dacy's law in porous media: v=-permeability/viscosity*Grad(Pl); assuming pg is uniform then we have v=permeability/viscosity*Grad(Pc); Pc is related to the saturation as Pc=f1(s); and permeability is related to saturation as Kp=Kp(absolute permeability)*f2(s); applying conservation equation we have the equation as follows Div(kp(abs)*f2(s)Grad(f1(s))=r(x,y) then Div(kp(abs)*f2(s)*d(f1(s))/ds)Grad(s))=r(x,y) that is all!

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