Couette flow with temperature-dependent viscosity

Numerical methods and mathematical models of Elmer
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maipe
Posts: 6
Joined: 02 Sep 2009, 19:11

Couette flow with temperature-dependent viscosity

Post by maipe »

Hi,

i would like to reproduce the analytical solution for Couette flow with temperature-dependent viscosity and i am getting a wrong result...
The setup is described in Turcotte and Schubert: Geodynamics, page 313. It is a steady flow between two boundaries, the left boundary moves with velocity v0 and has temperature T0, right boundary is fixed and has temperature T1. There are no heat sources, so the temperature profile is linear. Viscosity is C*exp(E/RT), where C,E and R are constants.
The solution should be
v/v0 (x)=(exp( (-E*(T1-T0))/(R * T0**2)*(1-x/h) )-1) / (exp( (-E*(T1-T0))/(R * T0**2) ) -1)
where h is the distance between the boundaries, 0<x<h.
I use
h=1,C=1, T0=1, T1=1.5, E=10, R=1, v0=1 (see attached sif-file). The result is quite different from the analytical solution (more like for E=6), but i don't know why... Any suggestions?

Thanks
Petra
Bench.sif
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mesh.grd
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Juha
Site Admin
Posts: 357
Joined: 21 Aug 2009, 15:11

Re: Couette flow with temperature-dependent viscosity

Post by Juha »

Hi Petra,

using Maple to solve

d(exp(10/(1+x/2)*dv/dx)/dx=0

i get

v:=a+b*((2+x)*exp(-20/(2+x))-20*Ei(1,20/(2+x)))

with v(0)=1,v(1)=0 we have

a ~ 1.017288049, b ~ -2256.783772

evaluating this with x=[0,1] seems to agree with ElmerSolver results. Am i missing something?

-Juha
maipe
Posts: 6
Joined: 02 Sep 2009, 19:11

Re: Couette flow with temperature-dependent viscosity

Post by maipe »

Hello Juha,

thank you very much for your answer. As always, you are right. The analytical solution is only approximate and (although shown in the book with these parameters) it is quite far from the correct solution in this case.

Thanks a lot again,
Petra
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