[tanmayagrawal7]

Originally Posted by FMDenaro

you are working with u and v constant and known? In this case, the solution is a simple linear wave propagating along the path-line, the grid-refinement should move dynamically

Yes. U and V equals one. I just want to check my local mesh refinement algorithm and want to make sure that it is giving better result than when there is no refinement. Then later on, I would change it to be a dynamic mesh once the procedure turns out to be right.

[FMDenaro]

Originally Posted by tanmayagrawal7

Yes. U and V equals one. I just want to check my local mesh refinement algorithm and want to make sure that it is giving better result than when there is no refinement. Then later on, I would change it to be a dynamic mesh once the procedure turns out to be right.

local steady refinement can not help improving this kind of solution

[tanmayagrawal7]

Originally Posted by FMDenaro

local steady refinement can not help improving this kind of solution

Why is that so professor? Say, I am validating my results along the centerline where there is a sudden jump of solution from 0 to 1. With local mesh refinement here along the center, should not I be able to manage to get a better solution?

[FMDenaro]

Originally Posted by tanmayagrawal7

Why is that so professor? Say, I am validating my results along the centerline where there is a sudden jump of solution from 0 to 1. With local mesh refinement here along the center, should not I be able to manage to get a better solution?

this jump will rapidly move far from the refined region

[tanmayagrawal7]

Originally Posted by FMDenaro

this jump will rapidly move far from the refined region

In my particular case with the boundary conditions that I am using, this jump remains in steady state. You can imagine a square with top and left sides on 1 and right and bottom sides on 0 initial value. At steady state, the center point of square is where the jump happens. You are right that in transient case, this will keep moving like a wave.

[FMDenaro]

your BC.s cannot be prescribed on all the edges of the box but only at left and bottom .....

[tanmayagrawal7]

Originally Posted by FMDenaro

your BC.s cannot be prescribed on all the edges of the box but only at left and bottom .....

Why is that so professor? I remember I have earlier solved 1D inviscid Burgers equation in which I had BC on both of the ends of domain. And how would I deal with the top and right two boundaries if this is the case? Periodic BC?

[FMDenaro]

Originally Posted by tanmayagrawal7

Why is that so professor? I remember I have earlier solved 1D inviscid Burgers equation in which I had BC on both of the ends of domain. And how would I deal with the top and right two boundaries if this is the case? Periodic BC?

that's wrong, the 1D Burgers equation requires only one BC. to be well posed.

[tanmayagrawal7]

Originally Posted by FMDenaro

that's wrong, the 1D Burgers equation requires only one BC. to be well posed.

For that case actually, I had used the initial condition and boundary conditions from the PhD thesis of Marsha Berger(who proposed adaptive mesh refinement for hyperbolic PDE that I want to use). But even with 2 BC, it got solved well.

[FMDenaro]

Originally Posted by tanmayagrawal7

For that case actually, I had used the initial condition and boundary conditions from the PhD thesis of Marsha Berger(who proposed adaptive mesh refinement for hyperbolic PDE that I want to use). But even with 2 BC, it got solved well.

I don't know such thesis but I know that the Cauchy problem requires only one BC to be well posed.
I strongly suggest to better study the character of the equations and the required boundary conditions

[tanmayagrawal7]

Originally Posted by FMDenaro

I don't know such thesis but I know that the Cauchy problem requires only one BC to be well posed.
I strongly suggest to better study the character of the equations and the required boundary conditions

Thanks professor! So in my two dimensional case, what kind of BC will I need on the other two edges?

[FMDenaro]

Originally Posted by tanmayagrawal7

Thanks professor! So in my two dimensional case, what kind of BC will I need on the other two edges?

you can prescribe the value of T only on the edges where the flow enters (left and bottom), no BC.s have to be prescribed when the flow leaves the domain