Mixed Order Mesh Curving: When Solution Accuracy Cannot Be Compromised!

Read the technical brief to learn about Mixed-Order Mesh Curving using Cadence Fidelity Pointwise.

When performing numerical simulations on complex systems, discretization schemes are necessary for the governing equations and geometry. In computational fluid dynamics (CFD) simulations, meshing is used to discretize system geometry and generate a set of points where the solution of governing equations can be computed. However, balancing the need for high accuracy, high resolution, and low computational effort in simulations is challenging. This challenge has led to the development of various meshing methods that can handle complex geometries without increasing the computational complexity. Among the various meshing methods, mixed-order meshing is a technique that uses high-degree polynomial curves to build a mesh for complex systems, providing higher accuracy than linear meshes.

Mixed-order mesh curving of an engine nacelle and pylon.

What Is a High-Order Mesh?

A high-order mesh is a type of mesh that uses a curve of a polynomial degree higher than one to connect adjacent mesh points. This is in contrast to a linear mesh where volume cells are constructed from straight lines connecting grid points. High-order meshing employs "mesh curving" by connecting grid points with a non-linear polynomial function, such as a second-degree quadratic function.

A flowchart of the mixed-order mesh curving process.

Why Is Mixed-Order Mesh Curving Preferred?

High-order mesh curving is difficult when the mesh contains a clustering of elements toward viscous boundaries. The edges and faces of interior elements must also be curved in response to the boundary element curvature to prevent element inversion. Research on the weighted condition number (WCN) smoothing used by Cadence Fidelity Pointwise permits mixed-order meshes to resolve geometry curvature. The elements can be elevated to a maximum polynomial of degree four (quartic) near highly curved geometry, while the elements remain linear far away from curved geometry. The mesh smoothing method uses a cost function to enforce desired element shapes and positive Jacobians across each element. Viscous mesh spacing is maintained as the elements are curved near the geometry.

Mixed-order meshes of the JFM – (a) Full view showing Q1-Q3 elements, (b) Cut at the wing tip trailing edge showing mixed-order Q1-Q4 elements.

 To learn more about Mixed-Order Mesh Curving using Cadence Fidelity Pointwise, read the technical brief:

Key Takeaways from the Technical Brief

• Generate high-quality meshes with lower element count for improved solution accuracy and reduced computation time.
• Insights on Weighted Condition Number (WCN) smoothing that permits mixed-order meshes to resolve geometry curvature.
• Mixed order mesh curving on two realistic, complex geometries – Juncture Flow model (JFM) and NASA High Lift Common Research Model (CRM-HL)