Nonstandard Discretizations for Fluid Flows (10w5041)

Objectives

Recent years have witnessed tremendous developments in several directions. Among those are the use of nonstandard finite elements like discontinuous Galerkin methods, divergence-conforming and nonconforming methods. Several new classes of stabilization techniques for advection-dominated flows have emerged: edge stabilization; residual- and entropy-based viscosity; and special fluxes for discontinuous Galerkin schemes. New approaches of turbulence have been proposed like subgrid viscosity, variational multiscale methods and large eddy simulation. More accurate time-stepping schemes, projection methods and fractional-step schemes have been discovered and preconditioning techniques have matured.

The ability to devise reliable and fast flow solvers requires in-depth knowledge of current developments in all directions listed above. As the field of CFD is ever expanding, most of the new discoveries are very specialized and suffer from long diffusion times to cross the entire community. The main objective of this workshop is to convene specialists who have brought improvements to the field so that they publicize their techniques to the other attendees. We expect this workshop to help maintaining the unity of a more and more diversifying field. The different research areas represented by the anticipated attendees have nevertheless sufficient intersections so that each attendee will benefit from of new ideas coming from other fields.

For instance researchers working on basic discretization and stabilization techniques will gain insight into applications. On the other hand, researchers developing solution methods for advanced applications will have access to new discretization techniques. Since there is also a conceptual similarity between variational multiscale methods and some stabilization techniques, we expect new ideas to emerge though exchanges between the specialists of these methods.

The workshop will bring together leading researchers in mathematical CFD. We expect to create a diverse group of participants from North America and Europe. The group will be a mix of senior and junior researchers, students, and postdoctoral fellows. The purpose will be to:

1. Identify the state-of-the-art nonstandard techniques for flow discretization and the contemporary areas of applications.

2. Formulate open questions and opportunities related to these techniques. Identify challenging applications ahead and possible further developments of these methods.

3. Promote collaborations among the leading groups in the field.