Finite diffeence and stream lines graph

[zeroground]

Homework Statement

i want to use finite difference methodolgyto determine the steady-state potential flow field in a two dimensional duct using a square mesh and get epsi at every grid node and graph the stream lines...any suggestions ?

Homework Equations

i've got an equation epsi(i,j) =1/4* epsi(i+1,j) + epsi(i-1,j) + epsi(i,j+1) + epsi(i,j-1)

The Attempt at a Solution

i have the boundary conditions at the entrance anf exit and the button and top of the duct ... how can i attach a file to show you the problem ?

 

[KataKoniK]

I would suggest the following steps to approach this problem:

1. Start by defining the problem clearly and making a list of all the known information, including the boundary conditions and any relevant equations.

2. Next, determine the type of finite difference method you will use. There are different types such as explicit, implicit, and Crank-Nicolson. Choose the one that is most suitable for your problem.

3. Once you have chosen the method, create a grid or mesh for your problem. In this case, a square mesh would be suitable. Make sure to include all the boundary points and label them accordingly.

4. Use the given equation to calculate the potential at each grid point. This will give you a set of equations that you can solve simultaneously using a numerical method such as Gaussian elimination or Gauss-Seidel method.

5. Once you have solved the equations, you will have the potential values at each grid point. Use these values to calculate the flow field and plot the streamlines.

6. Finally, analyze the results and make any necessary adjustments or improvements to your method.

As for attaching a file, you can use a file-sharing platform or include a link to the file in your forum post. Make sure to provide clear instructions on how to access the file.

 

[Mene]

I would suggest using the finite difference method to solve for the steady-state potential flow field in the two-dimensional duct. This method is commonly used in fluid dynamics to approximate solutions to differential equations. It involves discretizing the domain into a grid and using finite difference equations to approximate the derivatives at each grid point.

To graph the stream lines, you can use the values of epsilon (ε) at each grid node to determine the direction and magnitude of the flow. The stream lines can then be plotted using a vector field plot or by connecting points with the same epsilon value. This will give you a visual representation of the flow field in the duct.

As for attaching a file, you can upload it to a file sharing website and provide the link in your post. Alternatively, you can also include relevant equations and diagrams in your post to help illustrate the problem.