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

  • compare_upwind_20x20
  • compare_upwind_40x40
  • compare_upwind_80x80

 

Quality and quantity solution of structured mesh (0°)

  • GaussUpwind_upwind_20x20
  • GaussUpwind_upwind_40x40
  • GaussUpwind_upwind_80x80
  • upwind_research_2

 

Quality and quantity solution of structured mesh (45°)

  • GaussUpwind_upwind_20x20
  • GaussUpwind_upwind_40x40
  • GaussUpwind_upwind_80x80
  • upwind_research_1

 

Quality and quantity solution of unstructured mesh

  • upwind_20x20
  • upwind_40x40
  • upwind_80x80
  • upwind_research_3

 

Quality and quantity solution of polygon mesh

  • upwind_20x20
  • upwind_40x40
  • upwind_80x80
  • upwind_research_4
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