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26.4.1 Gradient Adaption Approach

Solution-adaptive grid refinement is performed to efficiently reduce the numerical error in the digital solution, with minimal numerical cost. Unfortunately, direct error estimation for point-insertion adaption schemes is difficult because of the complexity of accurately estimating and modeling the error in the adapted grids. A comprehensive mathematically rigorous theory for error estimation and convergence is not yet available for CFD simulations. Assuming that maximum error occurs in high-gradient regions, the readily available physical features of the evolving flow field may be used to drive the grid adaption process.

Three approaches for using this information for grid adaption are available in FLUENT:

The length scale is the square (2D) or cube (3D) root of the cell volume. Introducing the length scale allows resolution of both strong and weak disturbances, increasing the potential for more accurate solutions. However, you can reduce or eliminate the volume weighting by changing the gradient Volume Weight in the Grid Adaption Controls panel (see Section  26.12 for details).

Any of the field variables available for contouring can be used in the gradient adaption function. These scalar functions include, both geometric and physical features of the numerical solution. Therefore, in addition to traditional adaption to physical features, such as the velocity, you may choose to adapt to the cell volume field to reduce rapid variations in cell volume.

In addition to the Standard (no normalization) approach formerly used by FLUENT, two options are available for Normalization [ 117]:

Example of Steady Gradient Adaption

An example of the use of steady gradient adaption is the solution of the supersonic flow over a circular cylinder. The initial mesh, shown in Figure  26.4.1, is very coarse, even though it contains sufficient cells to adequately describe the shape of the cylinder. The mesh ahead of the cylinder is too coarse to resolve the shock wave that forms in front of the cylinder. In this instance, pressure is a suitable variable to be used in gradient adaption. This is because there will be a jump in pressure across the shock. However, several adaptions are necessary before the shock can be properly resolved. After several adaptions the mesh will be as shown in Figure  26.4.2.

A typical application of gradient adaption for an incompressible flow might be a mixing layer, which involves a discontinuity.

Figure 26.4.1: Bluff-Body Mesh Before Adaption

Figure 26.4.2: Bluff-Body Mesh after Gradient Adaption

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