**Making geometry models suitable for CFD meshing is often a time-consuming bottleneck in CFD analysis. Here we will discuss why this is so and some ways to alleviate the problems.**

NASA’s CFD Vision 2030 Study stated that “most standard CFD analysis processes for the simulation of geometrically complex configurations are onerous.” A major factor contributing to this perception is the preparation of geometry models for mesh generation, a task deemed a “significant bottleneck” in CFD workflows.

#### Boundary Representation

Boundary representation is the method of describing a solid object implicitly from its boundary and generally consists of two sub-representations: geometry and topology. Geometry describes individual shapes such as points, curves, and surfaces. Topology describes the entities that limit the portion of each geometric shape and the interconnections between those limited shapes.

**Analytic Geometry**

Geometry models produced in mechanical computer-aided design (MCAD) software are referred to as analytic boundary representations. The surfaces can be explicit and piecewise or implicit. The predominant form of parametric spline used in MCAD software is NURBS (Non-Uniform Rational B-Spline).

A T-Spline is a spline with a partially empty parametric space; the spline’s control points need not be defined at each parametric (u,v) coordinate. In general, a T-Spline model can consist of fewer surfaces than a NURBS model on the same shape. A U-Spline (Unstructured Spline) is a further generalisation of NURBS that are defined on triangular unstructured meshes versus the structured grid that is the rectangular parametric space of a NURBS or T-Spline.

Subdivision (Sub-D) is a method for modelling freeform surfaces that starts with a coarse mesh and through recursive point insertion achieves a limit surface that either interpolates or approximates the points in the original coarse mesh.

**Discrete Geometry**

Geometry models in the form of explicit surface meshes, independent of degree or element type, whether originally created for rendering, 3D printing, simulation, etc., are referred to as discrete boundary representations.

Discrete models can be produced by most CAD software (by tessellating an analytic model). There are other situations where the source of discrete models are 3D scans and extant meshes. 3D scans of an object allow the as-built versus the as-designed object to be represented for simulation. 3D scans also capture an object in its loaded configuration such as the upward flex of an aircraft’s wings in flight.

It is important to understand that analytic geometry has effectively unlimited resolution, but discrete geometry is limited to the resolution of the point density used to describe the shape. In other words, you can evaluate a NURBS surface anywhere and get coordinates that lie on the surface, but when you evaluate a discrete surface, you get a shape defined by linear interpolation between the known discrete points.

#### Boundary Topology

Topology is a mapping of logical connections that unifies a collection of subsets of geometric entities into a whole, often called a solid model or just a solid.

The bounding (limiting) of surfaces in a B-Rep topology is accomplished through an operation called trimming. This operation imprints curve(s) into a surface’s parametric space and limits the surface to the portion of the parametric space bounded by that curve and others. The resulting trimmed surface has a non-rectangular parametric space which affords it a great deal of flexibility in modelling complex shapes.

**Volumetric Representation**

Volumetric representation is the method of describing a solid object explicitly from a series of solid, space-filling primitives.

Constructive Solid Geometry (CSG) is the method of taking solid primitives and combining them hierarchically using the standard Boolean operations: union, intersection, and difference. The individual solid primitives are typically trivial shapes such as spheres and blocks, but can be arbitrarily complex.

Spatial occupancy modelling involves “digitising” the region of interest into pixels (2D) or voxels (3D). The relative properties of adjacent pixels are used to define boundaries within the region. X-ray, MRI, and CT scan are examples of spatial occupancy models.

Implicit geometry modelling defines a shape by an implicit function that evaluates to zero on the shape’s surface, a negative value on its interior, and a positive value elsewhere.

**Originating Intent & Software**

A geometry model may be created specifically for the purpose of simulation. Whether or not this model is derived from a master model in MCAD software, it will typically include simplifications and abstractions that vary based on the type of simulation to be performed (e.g., solid mechanics, fluid dynamics, electro-magnetics).

Simulation models are often created using software other than MCAD, such as software developed in-house or commercial off-the-shelf (COTS) software. This is especially true during the conceptual design phase when software tools like these may be the predominant tool for generating the outer mold line (OML).

In order to circumvent the complexity associated with using geometry models created in MCAD software, many organisations utilise design software tailored to their specific application. Notable among these tools for aerospace applications are OpenVSP [1] and ESP [2].

*Pointwise, Inc. is solving the top problem facing computational fluid dynamics (CFD) today – reliably generating high-fidelity meshes. The company’s Pointwise software generates structured, unstructured, overset and hybrid meshes; interfaces with CFD solvers such as CFD++, ANSYS FLUENT®, STAR-CCM+®, OpenFOAM®, and SU2 as well as many neutral formats, such as CGNS; runs on Windows, Linux, and Mac, and has a scripting language, Glyph, that can automate CFD meshing. Manufacturing firms and research organizations worldwide have relied on Pointwise as their complete CFD preprocessing solution since 1994.*

*Pointwise is a registered trademark of Pointwise, Inc. in the USA and the EU. Pointwise Glyph, T-Rex and Let’s Talk Meshing are trademarks of Pointwise, Inc. All other trademarks are property of their respective owner.*

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