Gauss Linear Scheme (2. Order)

The scheme numerical scheme named Gauss linear gives one the ability to reach more accurate solutions. Compared to the 1. order Gauss Upwind scheme it can produce nonphysical results. That means, the calculated value of the scalar Φ can be outside the physical range. In our case the range is between [0:1]. One can see that some points are lower than zero and higher than one. In the case of an unstructured grid the scheme is totally unstable and is diverging. The values of the scalar grow and blow up (demonstrated in the video). It is well known that the Gauss Linear scheme is unstable and can give unphysical results. To avoid such effects, one should use limited schemes; J.H. Ferziger and M.Perić.

 

Quantitative solution

  • compare_linear_20x20
  • compare_linear_40x40
  • compare_linear_80x80

 

Quality and quantity solution of structured mesh (0°)

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  • linear_40x40
  • linear_80x80
  • linear_research_2

 

Quality and quantity solution of structured mesh (45°)

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  • linear_40x40
  • linear_80x80
  • linear_research_1

 

Quality and quantity solution of unstructured mesh
Notice that the scheme is unstable in this case. Have a look to the video. Some cells produce very unphysical results till the whole solution gets totally unstable and unphysical.

  • linear_20x20
  • linear_40x40
  • linear_80x80
  • linear_research_3

 

Quality and quantity solution of polygon mesh

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  • linear_40x40
  • linear_80x80
  • linear_research_4

 

Time history of the development of the unstable solution

 

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