A Regrid operation is specified by supplying a new number of grid points during a restart or continuation, which allow a new flame solution to begin from an initial guess based on the solution of a previous flame.

The steady-state solver, Twopnt, automatically refines the grid by adding points in regions where they are needed to resolve the first and second derivatives of the solution, using criteria controlled by the Gradient and Curvature grid parameters. However, Twopnt does not move or remove points. If it reaches a maximum number of points (internally defined by the dimensions), a warning message is printed and the adaptation is terminated. In some cases, then, it may be necessary to reduce the number of points when starting a new solution from a previous result. The Regrid operation redefines the solution guess on the user-specified number of mesh points.

The Regrid operation is different from the grid-point insertion operation performed by Twopnt. Both operations attempt to resolve the gradient and curvature in the solution, except that Twopnt considers all solution components, whereas Regrid only considers the temperature profile. Twopnt only adds points, leaving the old points as they were, but Regrid alters the location and solution of all the points interior to the boundaries. Regrid computes new locations for exactly the given number of points, and then interpolates the solution from the previous grid to obtain a new approximation of the solution. Regrid does not conserve any properties of the solution; in fact, it tends to smooth the solution by the error inherent in the interpolation.

Regrid redistributes a weighting function of the first and second derivatives of the temperature. The profiles of the other dependent variables are ignored on the assumption that the temperature profile defines the flame location well enough for the purposes of realigning the mesh for an initial condition. The redistribution uses a transformation from the physical coordinate to a new coordinate

(14–17)

with the weighing function,

(14–18)

Integration over the entire domain defines the constant

(14–19)

Integrating over a portion of the domain gives an expression for the point locations in -space

(14–20)

The new grid locations come by interpolation between the computed values of defined using the old mesh, onto a uniform mesh in -space. Since is constant on this uniform mesh, the solution to Equation 14–17 states that is constant, so the new values of will be concentrated where the weighting function is large.

Below is a sample set of parameters that would direct the Opposed-flow Flame Model to perform the Regrid operation during a restart:

These parameters are specified in the Cluster Properties Panel, when Restart problem-type is chosen. This sequence will create a new solution guess on 20 points, devoting 60 percent of the points to resolving gradients, with equal weighting of gradient and curvature in the temperature profile. From experience, we recommend a value greater than or equal to 1 for the gradient to curvature adaptation ratio. Depending on the resolution of the existing solution, the percent of grids used in the regrid process should be in the neighborhood of 50%. Note that using 0 percent grids for regrid results in a uniform mesh.