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Gradient scheme example

Introduction​

The test case comprises a 2-D section comprising extruded triangle cells. An initial field is assigned the mesh cell centre values such that the computed gradient should take the value of 1 in each co-ordinate direction. By changing the choice of gradient scheme we can observe how each performs.

Case set-up​

Gradient schemes under test:

  • Gauss linear
  • Gauss pointLinear
  • leastSquares

Interpolation schemes under test:

Boundary conditions​

Only the left and right domain boundaries are set to physical patch types; the remainder are set to the empty constraint to enforce the 2-D system.

Mesh​

The mesh comprises extruded triangle cells with low non-orthogonality with average and maximum values of 7 and 26 deg, respectively.

Scheme controls​

grad(Cc)        <scheme>

Results​

The following images show the percentage error of the magnitude of the gradient of the cell centres, defined as:

error=100∣∇(Cc)∣−20.520.5 \textrm{error} = 100 \frac{\left|\grad(C_c)\right| - 2^{0.5}}{2^{0.5}}

The range is set to +/- 10% for all images.

Unlimited​

Gauss linear
Gauss point linear
Least squares

Cell limited​

Gauss linear
Gauss point linear
Least squares

Face limited​

Gauss linear
Gauss point linear
Least squares

Multi-directional cell limited​

Gauss linear
Gauss point linear
Least squares

Multi-directional face limited​

Gauss linear
Gauss point linear
Least squares