I cant understand the equations written in trixi

Chowdhury_MD_Irtiza · June 9, 2024, 4:41am

Hello, my professor gave me a problem to solve, and in order to solve the problem, I have to modify the compressible navier-strokes equation 2D that already in trixi documentation into fully compressible reactive unsteady 2D navier-strokes equation. I am very new to trixi and julia and even programming, I just learned trixi and julia last week from tutorials, I have been looking into the compressible navier strokes equation codes from yesterday, but until now I could not figure out how to modify the code for my own useage. Please help me someone in my issue. I am freaking out inside.

ufechner7 · June 9, 2024, 4:56am

Which code are you talking about?

Chowdhury_MD_Irtiza · June 9, 2024, 5:03am

Trixi.jl/src/equations/compressible_navier_stokes_2d.jl at main · trixi-framework/Trixi.jl · GitHub

I have to modify this compressible navier strokes equation into fully compressible unsteady navier strokes equation.

ufechner7 · June 9, 2024, 5:14am

Do you have a test case? I would always start with a simple test case.

And do you have a mathematical formulation of the “compressible unsteady navier strokes equation”?

Chowdhury_MD_Irtiza · June 9, 2024, 5:44am

Yes I have the mathematical formula of the fully compressible navier-strokes equation. And I have a test case also. I am attaching the mathematical formulation of the fully compressible unsteady navier strokes equation in this chat

Chowdhury_MD_Irtiza · June 9, 2024, 5:45am

I have to modify the equation based on this screenshot

mkitti · June 9, 2024, 5:57am

It might be useful to look at the rendered documentation here:

You should see something that looks like this:

In particular, the first three equations seems to be implemented here:

github.com

trixi-framework/Trixi.jl/blob/2043cfe3f79de2b77124c13d57de96a8ddf0ea52/src/equations/compressible_navier_stokes_2d.jl#L148-L200


      
          function flux(u, gradients, orientation::Integer,
                        equations::CompressibleNavierStokesDiffusion2D)
              # Here, `u` is assumed to be the "transformed" variables specified by `gradient_variable_transformation`.
              rho, v1, v2, _ = convert_transformed_to_primitive(u, equations)
              # Here `gradients` is assumed to contain the gradients of the primitive variables (rho, v1, v2, T)
              # either computed directly or reverse engineered from the gradient of the entropy variables
              # by way of the `convert_gradient_variables` function.
              _, dv1dx, dv2dx, dTdx = convert_derivative_to_primitive(u, gradients[1], equations)
              _, dv1dy, dv2dy, dTdy = convert_derivative_to_primitive(u, gradients[2], equations)
          
              # Components of viscous stress tensor
          
              # (4/3 * (v1)_x - 2/3 * (v2)_y)
              tau_11 = 4.0 / 3.0 * dv1dx - 2.0 / 3.0 * dv2dy
              # ((v1)_y + (v2)_x)
              # stress tensor is symmetric
              tau_12 = dv1dy + dv2dx # = tau_21
              # (4/3 * (v2)_y - 2/3 * (v1)_x)
              tau_22 = 4.0 / 3.0 * dv2dy - 2.0 / 3.0 * dv1dx

This file has been truncated. show original

Chowdhury_MD_Irtiza · June 9, 2024, 6:08am

thanks for the shared link, I need to modify the number three equation and have to add number 4 equation to make it fully compressible navier-stroke equation from compressible navier strokes equation. Can you help me to understand or share some documentation that can help me to understand how to add or modify the equation? It will be a big help. I am trying to figure out this from yesterday, but since I am very new to these I cant seems to understand anything, which is making me frustrated.

The equation that I have to modify and add I am sharing here

carstenbauer · June 9, 2024, 6:15am

cc @sloede @ranocha

Chowdhury_MD_Irtiza · June 9, 2024, 6:20am

please help me, someone

Chowdhury_MD_Irtiza · June 9, 2024, 6:27am

for more better understanding why I need to modify the equation, I am uploading the paper’s abstract which i am trying to solve in trixi, so that from abstract and governing equation anyone who will give their effort to help me can understand easily.
This is the governing equation

Chowdhury_MD_Irtiza · June 9, 2024, 6:28am

This is the abstract of the paper.

ranocha · June 10, 2024, 6:43pm

Based on what you describe, it looks like you need to write a new set of equations. We have several tutorials describing this process, e.g.,

Do you have any specific questions we hay help to answer?