NASA’s work in advanced aeronautics and space vehicle development relies on advanced Computational Fluid Dynamics (CFD) codes such as FUN3D that rely on numerical solution of equations of motion over a discrete mesh of points in three dimensions. A judicious placement of points is required to optimize computing efficiency without greatly reducing the sensitivity and accuracy of the calculations. Rapid generation of such a mesh and its subsequent adaptation to better resolve the problem physics are critical to the application of CFD to complex real-world problems of interest.

What are the Challenges?

Improved mesh generators are needed to support programs in aerothermodynamics and fluid dynamics in general. More specifically, an anisotropic 3D mesh generator (or re-mesher) is needed that can be driven by a spatially varying metric tensor field, and which specifies mesh spacing along three orthogonal directions.

Highly anisotropic mesh about the complex Mars Phoenix Lander

The mesh generator must accommodate cell aspect ratio requests of at least 10,000:1 even in the presence of a curved metric tensor field to enable high Reynolds number finite-volume CFD applications. Furthermore, in regions of high anisotropy (not necessarily bounded by a vehicle surface), mesh cells should be dominantly layers of semi-structured hexahedra or triangular prisms to allow non-dissipative capture of bow shocks, boundary layers, free shear layers, wakes, contact surfaces, and so forth.

What is NASA Doing?

NASA currently conducts aerothermodynamic and fluid dynamics analyses of vehicles (heating rates, pressures, etc.) through the use of state-ofthe- art CFD codes. The mesh generation methods in use primarily rely on advancing front/layer, and/or Delaunay algorithms to provide the mesh of points needed to describe the vehicle and the surrounding domain of interest for the analysis. While current methods have been successfully applied to complex problems, clearly additional research and development is needed in the area of mesh generation to reduce human involvement and increase robustness.

We would like to provide uncertainty estimates (error bars) for the computational results delivered much like experimentalists do for their results. A critical component enabling this capability is mesh adaptation, whereby an existing mesh is adapted to improve the solution based on the problem physics and/or a solution error estimate. The criteria that drive the mesh adaptation are specified via a Riemannian metric tensor field. Within the field, a 3x3 (2x2 in 2 dimensions) symmetric positive definite tensor defines the desired local spacing constraints for the mesh whereby its eigenvalues represent the desired spacing along the direction of the corresponding eigenvectors.

Current mesh adaptation technology in use does not easily allow us to do this in the presence of high element anisotropy in three dimensions while maintaining element quality. If the desired mesh generator can be developed, we will gain control over spatial discretization errors for CFD codes. This will allow us to focus on physical modeling errors and automate the process of obtaining a solution for a given application with bounded discretization errors.

NASA’s immediate needs include CFD modeling of the exploration vehicles now under development to replace the shuttle for transport to the International Space Station and eventually for transport to the Moon and beyond, as well as advanced supersonic and hypersonic air vehicle development, both for NASA (Commercial) and military applications.

The astrophysics, climate analysis, and hemodynamics (blood flow) fields may also have a use for such a capability, i.e., other types of fluid dynamics applications. More Information

For more information, contact Dr. Bill Kleb at 757-812-1805 or This email address is being protected from spambots. You need JavaScript enabled to view it..