AMMCS-2011 Semi-Plenary Talk:

Towards a Robust, Multi-Domain, Energy Stable WENO Formulation for High Speed Flows

by Mark Carpenter

NASA Langley Research Center

Weighted Essentially NonOscillatory (WENO) schemes are routinely used to perform high resolution simulations of canonical problems containing discontinuities, and are extremely successful in this context. Because conventional WENO formulations have numerous structural and design constraints (e.g. structured meshes, accuracy, conservation, stencil biasing . . .), extension to complex geometries is problematic. Herein, we demonstrate a general multi-block WENO capability, based on uniformly accurate fourth-order and sixth-order, finite-domain, Energy Stable WENO (ESWENO) operators. The individual blocks feature boundary closures that maintain design accuracy, conservation and L2 stability, while accommodating full WENO stencil biasing. The adjoining blocks are coupled using interface penalties motivated by Internal Penalty and DG formulations. Test cases are presented that demonstrate the efficacy of the new multi-domain ESWENO approach on high speed flow problems.

This work is performed in conjunction with Dr. Nail K. Yamaleev (North Carolina A & T State University, USA, and Travis Fisher (NASA Langley Research Center, USA).

Mark H. Carpenter received a BSc in Chemistry from Bethel College in 1981, and PhD in Mechanical Engineering (combustion emphasis) from Carnegie-Mellon in 1986. After graduation he accepted a position at NASA Langley Research Center, Hampton VA, USA. He has worked at Langley continuously for nearly 25 years, with the exception of a sabbatical year (2006) serving as a visiting professor at Technical University of Delft, The Netherlands. His research interests include the development of 1) high-order finite difference and spectral methods, 2) high-order explicit and implicit temporal integrators and 3) linear and nonlinear solvers. The applications motivating this development over the past decade include DNS/LES of high speed, chemically reacting flows, boundary layer stability and transition phenomena, and acoustic liner development. He currently serves on the editorial board of Journal of Scientific Computing, and the advisory panel for the International Conference of Spectral and High-order methods.