Gauss Upwind Scheme (1st Order)
Using the Gauss Upwind Scheme will produce - so called - diffusive solutions. That means that the gradients of the scalar will be smooth and the resolution is not very accurate - compare J.H. Ferziger and M. Perić, and the book of R. Schwarze. However, this scheme is the only available numerical scheme that produces always physical values. So the value of Φ are always in between the physical interval [0:1]. As one can see, the diffusion occurs especially if there is an angle between the flow direction (direction of velocity vectors) and the surface normal vectors. If the flow field is parallel to the grid, no numerical diffusion occurs.
Quantity solutions between the meshes
Quality and quantity solution of structured mesh (0°)
Quality and quantity solution of structured mesh (45°)
Quality and quantity solution of unstructured mesh
Quality and quantity solution of polygon mesh