A first-order upwind scheme is stable and converges on almost any problem. The price is that its truncation error appears in the form of a diffusion term: you have added an artificial viscosity to the equations that has no counterpart in the physics.
What artificial diffusion does
- Smooths velocity and temperature gradients — the boundary layer looks thicker than it is
- Damps vortices — the wake comes out shorter
- Delays the separation point, or erases it altogether
- Exaggerates mixing — concentration and temperature fields come out too uniform
The effect diminishes as the mesh is refined, but it is then entangled with mesh error: performing a grid independence study on a first-order solution means measuring two errors at once. See the grid independence note.
Alignment with the flow makes it worse
Artificial diffusion is generated most where the flow meets the cell face at an angle. On a hexahedral mesh aligned with the flow the effect is small; on a tetrahedral mesh that cannot be aligned it is far larger. Scheme choice and cell type therefore cannot be considered separately. See the cell type note.
Correct use
First order is a starting tool, not a solution. Use it for the first few hundred iterations to settle the field, then switch to second order and converge there.
Second-order schemes can produce oscillations at sharp gradients; a limiter is used to suppress them. A limiter carries its own cost — an overly aggressive one reduces the solution locally back to first order. See the gradients and limiters note.
What belongs in the report
The order the final solution was obtained with. Without that single line the result is not reproducible and the phrase "grid independent" loses its meaning.
References
- Patankar, S. V. (1980). Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing. ISBN 978-0-89116-522-4.
- Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6
- Celik, I. B., Ghia, U., Roache, P. J., Freitas, C. J., Coleman, H. & Raad, P. E. (2008). Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. Journal of Fluids Engineering, 130(7), 078001. DOI: 10.1115/1.2960953