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Old   October 19, 2005, 14:31
Default About the solution of a simplified two-phase model
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maximus
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hi,i am trying to solve a simlified two-phase model for the dilute droplets motion in the air. It's derived from the traditional Eulerian two-phase model in which alfa represents the volume fraction of liquid./ (1) /The continuum and momentum equations are as below(for steady problems): par(alfa*u)/par(x)+par(alfa*v)/par(y)=0, par(alfa*u)/par(x)+par(alfa*v*u)/par(y)=Cu*alfa, par(alfa*v)/par(x)+par(alfa*v*v)/par(y)=Cv*alfa. /(2)/ if above equations are written into no-conservative form,it can be seen that the continuum equation can be decoupled from the momentum equatons . So I solve the momentum equations to get u and v firstly,then deal with the continuum eqution to get alfa. /(3)/I try to discretize the equations with FVM,and use the high resolution schemes to deal with the convection terms.but I found that alfa is difficult to converge and there exists some oscillations even when I use the upwind scheme. I read some relative paper on this topic, and most of them use the FEM to discritize the equations and adopt the artificial viscosity or SUPG term to stablize the solution. /(4)/Because of the lack of experience to solve this kind of hyperbolic problem, so I don't know how to go ahead. I wonder if there are some methods to stablize the solution when I use the FVM to discritize the equations. I will be grateful for any suggestions! MAXIMUS

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Old   October 20, 2005, 03:42
Default Re: About the solution of a simplified two-phase m
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upwind
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It is curious that pressure does not appear in your equation. Can you mention the reference where these governing equations are derived.
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Old   October 20, 2005, 05:01
Default Re: About the solution of a simplified two-phase m
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maths
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Have a look to this absolutely interesting....the model is there already.....

http://www.math.ntnu.no/conservation/2003/026.html

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Old   October 25, 2005, 12:03
Default Re: About the solution of a simplified two-phase m
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maximus
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yes,pressure term does not appear in this equations because it is assumed that the pressure's effect on the droplets motion is neglected. you can look the paper below: http://www.newmerical.com/Scientific..._MULTISHOT.pdf. I find the eigenvalues of the Jcobian matrix of these equations are equal to each other: write the equation in the form: par(Q)/par(t)+par(F)/par(x)+par(G)/Par(y),and the Jacobian Matrix A=par(F)/par(Q),B=par(G)/par(Q). I find the three eigenvalues of A are lemda(1,2,3)=u, and lemda(1,2,3)=v for Matrix B. So maybe it's not a rigorous hyperbolic equations?

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