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### Gradient term in Navier Stokes equations

In the settings for solving methods, this term is known as Gradient and is divided into three methods:

1-Green-Gauss Cell-Based

In this method, the gradient value is performed on the cell surface by intermingling on two adjacent cells, and it can be said that in calculations the amount of gradient on the surface, two adjacent cells are involved. This method overestimates dispersed amounts. Although it may be used in some simulations, it is not very accurate. The low computational cost is one of the benefits of this method.

2-Green-Gauss Node-Based

In this method, the amount of gradient is carried out on the cell surface using the values of adjacent nodes. Since the FLUENT software is based on the cells and the nodes are not available in cell-based simulations, the average value of that node should be calculated using the values of the adjacent cells of each node. Thus, the adjacent cells involved in the calculations is larger than the Cell-Based method and using more cells in calculating the gradient term, so the simulation accuracy increases. The main problem in this method is its higher computational cost than other methods. This method is especially useful for simulating flow on sharp corner elements. It’s better not to be used on high-quality grids with proper angles and shapes because of high computational costs.

3-Least Square Cell-Based

This method, like the first method, calculates gradient values using adjacent surface cells. The difference is in the use of a change function based on network geometry. The coefficients of this function are calculated by the minimum sum of squares. Its accuracy is higher than the Cell-Base base method and its cost is lower than the Node-Based method. The precision of this method is comparable to the elements with sharp angles and deformed with the Node-Base method. However, it does not have a high computational cost over the Node-Based method, which is why the new software versions are considered as the default option.

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