The mission of the Advanced Numerical Simulation Laboratory at the University of British Columbia is to improve computational techniques for the solution of partial differential equations, with a particular interest in application to transonic aerodynamics, where improved methodology for flow solution continues to bring higher-fidelity simulation into the engineering design loop. More specifically, members of the group work in three primary areas: high-order accuracy methods on unstructured meshes; unstructured mesh generation and refinement, especially reducing the required amount of human input; and the interaction between mesh quality and solution accuracy. The team working in the lab is interdisciplinary: knowledge of aerodynamics, computer science, and mathematics are all valuable to the project.
Our recent work on higher-order accurate unstructured mesh finite volume methods has demonstrated that high-order methods are at least as efficient in CPU and memory use as second-order methods in computing solutions to simple problems in transonic aerodynamics. We are currently working to extend these results to three-dimensional, turbulent flows. In addition, because our high-order flow solver is more efficient than second order flow solvers, we expect --- and are working to demonstrate --- that our higher-order optimization scheme will also be more efficient than a corresponding second-order scheme.
As computers and solution algorithms continue to improve, the problem of mesh generation and adaptation becomes even more of a bottleneck in numerical simulation. Our goal in this area is to continue to reduce human input from the process by enabling automatic generation of high-quality isotropic meshes from CAD data, nearly automatic anisotropic mesh generation and automatic anisotropic mesh adaptation based on local error. In addition, we are working with the Interoperable Tools for Advanced Petascale Simulations (ITAPS) consortium in the US to develop a standard interface for interaction between solution algorithms and mesh data, both in serial and in parallel, to reduce the burden on application programmers to adopt new techniques in mesh generation and adaptation.
A new research area for the lab is the exploration of the interaction between mesh quality and discretization error. Surprisingly little is known about this topic, most of it anecdotal. In the near future, we will investigate --- both analytically and using numerical experiments --- the effects of local variations in cell size and shape on the accuracy of solution representation and discretization. Our long-term goal is to develop guidelines for mesh generation to improve the accuracy of particular discretization schemes on the resulting meshes.