The open source CFD toolbox

# 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

• 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:

$\textrm{error} = 100 \frac{\left|\grad(C_c)\right| - 2^{0.5}}{2^{0.5}}$

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

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