27.4.1 Dynamic Gradient Adaption Approach

The dynamic gradient adaption executes the gradient adaption automatically. Though all options of gradient adaption are valid for the dynamic gradient adaption, some specific settings are recommended:

In the Gradient Adaption Dialog Box

• Turn on Refine and Coarsen options.

• The Normalize per Zone enables zonal normalization for the dynamic adaption. See Section  27.3.1 (item 7) for details.

• For Normalization, use either the Scale or the Normalize option.

    The non-normalized values of the gradient or the curvature of a variable (obtained by selecting Standard for the Normalization) are generally strongly solution-dependent, and therefore would require re-adjustment of the Coarsen Threshold and Refine Threshold as the solution proceeds.

• For dynamic adaption, scaling is preferred if you wish to resolve regions of small values of the gradient (or curvature/isovalues) accurately, in addition to the region of highest gradient (or curvature/isovalues).

    Scaling does not take very high values of the gradient or curvature as much into account as does the normalization.

• The starting values for Refine Threshold and Coarsen Threshold are 1e10 and 0 respectively.

    The more refinement you want, the smaller these values should be.

• Specify the Interval between two consecutive automatic mesh adaptions. Depending on whether you are performing a steady state or a time dependent solution, specify Interval in iterations or time steps respectively.

  This value depends on the type of problem solved and the time step used (where applicable). For steady state problems, values of 100 or higher are reasonable and for time dependent problems, values of 10 or lower are often required.

    If you are using the density-based explicit solver with explicit transient formulation, your input will be in number of iterations.

In the Mesh Adaption Controls Dialog Box

• Set values for Min # of Cells, Max # of Cells, Max Level of Refine or Min Cell Volume.

  The limits for the Min # of Cells and Max # of Cells can affect the Coarsen Threshold and Refine Threshold values. If either the Min # of Cells or the Max # of Cells are violated, the Coarsen Threshold or the Refine Threshold are adjusted to fulfill the limits for the Min # of Cells or the Max # of Cells.

• The default value for Max Level of Refine is 2, which is a good start for most problems. If required, you can increase this value.

  Even in a 2D problem, the default value of 2 can increase the number of cells by a factor of 16, in the adapted regions. A value of zero leaves this parameter unbounded: in this case you should use a suitable limit for Min Cell Volume.

Examples of Dynamic Gradient Adaption

Example 1: Steady state problem.

Consider a supersonic flow over the blunt body. To determine the wave drag for such problem, first resolve the shock wave. Start with a coarse mesh and set up dynamic adaption. As you start iterating the solution, the solver will produce a blurred shock, probably in an incorrect location. After the adaptions, the shock will become sharper and move into the correct location.

Example 2: Time dependent problem.

Consider a traveling shock wave. To determine the precise pressure amplitudes and arrival times at a number of locations, you need to resolve the shock wave over the time, so that you can maintain the correct shock strength and its location. Dynamic adaption is efficient in this case, as it refines the mesh near the shock and at the same time it coarsens the mesh wherever needed.