[mihirmakwana6]

Consider a square cavity filled with air ( Pr = 0.71 ) of side L .

B.C : adiabatic on TOP and BOTTOM wall ;
Constant temp. of left and right wall ( T_left > Tright )

Mach no. of the flow is approx 1.5e-3 .

so, here speed of fluid flow is much slower than that of speed of sound.

Thus , Can a solution be obtained by directly solving the continuity, momentum and energy equation.

by directly i mean that solving in the following manner

http://i.imgur.com/wnv46Po.jpg

AND then repeating this process till convergence


Please reply.

Thanks in advance

[FMDenaro]

Originally Posted by mihirmakwana6

Consider a square cavity filled with air ( Pr = 0.71 ) of side L .

B.C : adiabatic on TOP and BOTTOM wall ;
Constant temp. of left and right wall ( T_left > Tright )

Mach no. of the flow is approx 1.5e-3 .

so, here speed of fluid flow is much slower than that of speed of sound.

Thus , Can a solution be obtained by directly solving the continuity, momentum and energy equation.

by directly i mean that solving in the following manner

http://i.imgur.com/wnv46Po.jpg

AND then repeating this process till convergence


Please reply.

Thanks in advance

From a mathematical point of view no matter in using the full compressible system. Actually the numerical solution is hill-conditioned as you solve for a condition similar to have dp/d rho -> Inf.
The system needs to be pre-conditioned or, much better, reduced to the incompressible form

[mihirmakwana6]

Originally Posted by FMDenaro

From a mathematical point of view no matter in using the full compressible system. Actually the numerical solution is hill-conditioned as you solve for a condition similar to have dp/d rho -> Inf.
The system needs to be pre-conditioned or, much better, reduced to the incompressible form

sir, won't the acoustic waves in the flow create any sort of problems (say large velocity fluctuations), if we solve the full compressible system.

[FMDenaro]

Originally Posted by mihirmakwana6

sir, won't the acoustic waves in the flow create any sort of problems (say large velocity fluctuations), if we solve the full compressible system.

preconditioning is what avoid this problem, for example see:

https://www.sharcnet.ca/Software/Flu...g/node1003.htm

[mihirmakwana6]

Originally Posted by FMDenaro

preconditioning is what avoid this problem, for example see:

https://www.sharcnet.ca/Software/Flu...g/node1003.htm

ok. Thankyou.

Is there a paper you know that solves compressible equations in the manner

http://i.imgur.com/wnv46Po.jpg

[FMDenaro]

Originally Posted by mihirmakwana6

ok. Thankyou.

Is there a paper you know that solves compressible equations in the manner

http://i.imgur.com/wnv46Po.jpg

for the thermal cavity flow, I remember only papers using the incompressible flow modelled with Bousinnesq

[mihirmakwana6]

ok. fine.

Sir, I have one basic doubt. As the speed of sound is quite high compared to the flow velocity, there will be waves in the system. So, to avoid this , as you mentioned preconditioning can be used. So are we loosing any vital information by applying preconditioning.

So, its like we start from state A ( initial condition ) and want to reach to state B
( steady state ) . Both the methods ( i.e directly solving compressible equations AND preconditioning ) will takes us from A to B. but what about the values attained by the variables ( u , p , rho ,T ) in between the states A and B.

The intermediate states given by both the methods will be very much different right ?

So, are we actually loosing out information by applying preconditioning ?

Thus the question is that are we sort of unknowingly throwing away legitimate transience by using preconditioning ?

[FMDenaro]

using a transient model has the same goal both for the fully compressible and incompressible models, any variable subject to the time-dependency must be solved in a way as accurate as possible to give the correct temporal dynamics....It is the chosen model that can disregard some physical information, as the acoustic waves in the incompressible model, the high temperature variation in the Bousinnesq model and so on...

[mihirmakwana6]

Originally Posted by FMDenaro

using a transient model has the same goal both for the fully compressible and incompressible models, any variable subject to the time-dependency must be solved in a way as accurate as possible to give the correct temporal dynamics....It is the chosen model that can disregard some physical information, as the acoustic waves in the incompressible model, the high temperature variation in the Bousinnesq model and so on...

sir so as the model disregards some physical information, won't that provide solutions different than the actual one .