Designing High-Order Methods for Solution Gradients: A Radical but Effective Approach

Speaker: 

Dr. Alireza Mazaheri — NASA Langley Research center

Abstract:

In this talk, we discuss high-order methods that are constructed with a reformulation of the target governing equations. The proposed methodology allows us to design high-order schemes that are capable in producing accurate and noise-free solution gradients on highly irregular elements. The reformulation strategy makes the governing equation hyperbolic in pseudo-time but does not change the physics of the phenomenon that is described by the target equation. We first present the reformulation strategy for a general time-dependent advection-diffusion problems (e.g., Navier-Stokes or Viscous Burger Equation), and introduce a different reformulation strategy fordispersive Partial Differential Equations (PDEs), such as those appear in hydrodynamics, coastal engineering, Soliton wave analysis, nonlinear optics, etc. Then, we walk through development of high-order schemes on the platform of these reformulated governing equations, and show that the resulting proposed high-order schemes lead to a same order of accurate solution and solution gradients (and Hessian or second-derivatives for the dispersive PDEs) on highly irregular unstructured grids. Furthermore, the predicted solution gradients are accurate and noise-free. We finish the discussion with some suggestions for further advancements.

Bio:

Dr. Alireza Mazaheri is a Computational Aerothermodynamicist at NASA Langley Research center since 2006. Priorto his current position, he worked at Parsons Inc. (as a research engineer), was a postdoctoral fellow at Pittsburgh University (from 2004-2005) and a National Research Council (NRC) postdoctoral fellow at the US Department of Energy (from 2003-2004). He earned PhD from Clarkson University in Mechanical Engineering, MS from Shiraz University in Computational Thermo-Fluid Engineering, and BS from Guilan University in Fluid Mechanics. Alireza has been involved in several NASA programs/projects, including the Space Shuttle, Orion Multi-Purpose Crew Vehicle (MPCV), Dream Chaser, Hypersonic Inflatable Aerodynamic Decelerator (HIAD), High Energy Atmospheric Reentry Test (HEART), etc. His current research interests are on development of high-order methods that are capable in producing accurate and noise-free solution gradients(e.g., velocity gradients, heat flux, shear stresses, etc.) on irregular tetrahedral elements.