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# Structured Grid Generation

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Pointwise's structured quadrilateral and hexahedral grid techniques are the best available and have been honed continuously since 1984 to generate the best quality grids with the ultimate in control over smoothness, clustering, and orthogonality.

The software begins with transfinite interpolation (TFI) algebraic techniques that automatically account for adherence to the geometry model where necessary. Several formulations of the TFI method are available including standard, linear, polar, and parametric.

## Elliptic PDE Smoothing

The cell quality of structured grids can be significantly improved by applying Pointwise's elliptic PDE methods. These methods iteratively solve Poisson's equation with control functions that can be fine-tuned at any time using the following techniques.

• Laplace (smoothness)
• Thomas-Middlecoff (clustering)
• Fixed Grid (smoothness)
• von Lavante-Hilgenstock-White (orthogonality)
• Steger-Sorenson (orthogonality)

Several formulations of the wall angle and wall spacing constraints are available with the von Lavante-Hilgenstock-White and Steger-Sorenson methods to ensure grids that meet your needs for how transverse grid lines meet boundaries.

The elliptic PDE smoothing technique can be applied to a surface grid (green) that spans multiple geometry model surfaces (pink) and still attain the desired levels of smoothness, clustering, and orthogonality.

The elliptic solver methods also feature support for several boundary condition types depending on whether you need the boundary points to remain fixed, slide along the shape, or float with the PDE solution.

The surface formulation of the elliptic PDE methods allows for surfaces to be constrained to the CAD geometry whether that be a single surface or span a collection of surfaces.

## Extrusion Methods for Structured Grids

Structured grids with high degrees of orthogonality and clustering control can also be created using Pointwise's hyperbolic PDE and algebraic extrusion methods. The extrusion methods start with one or more structured quadrilateral surface grids and extrude hexahedral volume grids. The extrusion can generate one volume grid per surface grid or surface grids can be grouped into larger faces for extrusion into a single block.

All of the extrusion methods also can be applied to 2D grids and surface grids constrained to CAD surfaces. In the latter case, the mesh marches across the entire geometry model, from one surface to the next.

The hyperbolic PDE method can rapidly generate structured grids that are smooth, clustered, and orthogonal, as illustrated by this single grid for a multi-element airfoil.

The hyperbolic method is especially well suited for CFD solvers that use overlapping grids but contains features to extrude multi-block abutting grids as well. In other words, a point to point interface can be maintained between adjacent abutting blocks.