Plotting solutions obtained by FVM
 

Hello,

A simple question.

In Finite-Volume Methods, it is assumed that solutions are stored at cell-center (e.g. centroid of triangle). But it seems that they are stored at vertices when plotted. For example, surface pressure distributions are usually displayed as a solution, where they are actually not located.

Do you usually compute nodal values as a post-processing in Finite-Volume Code, for instance by some averaging?

If yes, doesn't it affect the solution accuracy? (Solutions seem to diffuse after averaging)

Thank you,

Nishikawa

Re: Plotting solutions obtained by FVM
 

To compute the vertex values of a variable, one can extrapolate its value from the cell centre of each element to its vertices (e.g. using the gradient of variable). Then take averages where appropriate and you have the vertex values. For the vertices belonging to the boundary surfaces one should directly use the information about boundary conditions on this surface. Please notice that on some surfaces the averaging is not allowed. Simple example is a heat conduction problem on the surface separating two materials of different heat conductivities. If the materials are not in perfect contact with one another, there is a jump in temperature on this surface. There will be two values of temperature on this surface.

With correctly calculated gradients and proper account for boundary conditions, the above procedure does not affect accuracy of the solution.

regards

DML

Re: Plotting solutions obtained by FVM
 

Hi. I supose that all graphical software used for display results in surface form, use some kind of interpolation, bi-linear interpolation, Delaunay triangulation, or some finite-element type interpolation function, to obtain values where you don´t have specify data, so you will always have values of variable that you really didn´t calculated in your CFD program. From your comment, i can imagine that there is only a little problem, you are using values of pressure in one point(node) and values of coordinates in another one. The solution for this problem, if you are interest to plot the calculated values, you can calculate the cell-centered node coordinates and then associate them to the respective pressure value.

Good luck

Carlos Vilela

Re: Plotting solutions obtained by FVM
 

Thank you very much!

I found some ways to compute vertex values from cell-averages. And i was able to write a code with first order schemes.

For first-order accuracy, I think the following is OK. Considering median dual cell, I can determine the cell-average for the dual cell which can be obtained by

Sum over triangles that share vertex j of solution * (1/3 of the area of triangle), divided by the area of the median dual cell.

The solution looks OK. Now I'm planning 2nd order version.

Nishikawa