The main difference between each scheme is the number of the points considered to evaluate; more basically, first order considers one upstream point and second order considers two points. First order scheme is very fast compared to second order scheme; however it may cause you obtain inaccurate results and false diffusion. I suggest you consider second order scheme if you need to pick one of them. I suggest you refer to An Introduction to Computational Fluid Dynamics:The Finite Volume Method written by H. Versteeg & W. Malalasekera for more details.
You have to check on fluent guide to see the equations and the differences!
https://uiuc-cse.github.io/me498cm-fa15/lessons/fluent/refs/ANSYS%20Fluent%20Theory%20Guide.pdf
The main difference between each scheme is the number of the points considered to evaluate; more basically, first order considers one upstream point and second order considers two points. First order scheme is very fast compared to second order scheme; however it may cause you obtain inaccurate results and false diffusion. I suggest you consider second order scheme if you need to pick one of them. I suggest you refer to An Introduction to Computational Fluid Dynamics:The Finite Volume Method written by H. Versteeg & W. Malalasekera for more details.
What Hasan is written is right. You should always use second order upwind scheme since it is more accurate than the first order scheme. But, as a beginner you should run your simulation by using 1st order upwind scheme. Once, you got a converged solution, switch to 2nd order scheme. If your 1st order scheme is not converging, then 2nd order scheme will not converge.
2nd order scheme is more accurate but less stable. If you have a very good mesh, for example not too high aspect ratios and not too skew faces, you should not have problems using the 2nd order schemes. I would go for a 1st order if I'm unsure about my mesh quality and initial conditions
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