Seminar 2016-02 Alireza Mazaheri: Hyperbolic Method for Dispersive PDEs: Same High-Order of Accuracy for Solution, Gradient, and Hessian

Topic: 71st NIA CFD Seminar: Hyperbolic Method for Dispersive PDEs: Same High-Order of Accuracy for Solution, Gradient, and Hessian

Date: Wednesday, February 24, 2016

Time: 11:00am-noon (EST)

Room: NIA, Rm137

Webcast link:

Speaker: Dr. Alireza Mazaheri

Abstract: In this talk, we introduce a new hyperbolic first-order system for general dispersive partial differential equations (PDEs). We then extend the proposed system to general advection-diffusion-dispersion PDEs. We apply the fourth-order RD scheme of Mazaheri and Nishikawa [Computers and Fluids, 102 (2014), 131–147] to the proposed hyperbolic system, and solve time-dependent dispersive equations, including the classical two-soliton Korteweg-de Vries (KdV) and a dispersive shock problems. We demonstrate that the predicted results, including the gradient and Hessian (second derivative), are in a very good agreement with the exact solutions. We also show that the high-order RD scheme applied to the proposed system accurately captures dispersive shocks without numerical oscillations. We also verify that the solution, gradient and Hessian are predicted with equal order of accuracy.

Bio: Dr. Alireza Mazaheri is a Computational Aerothermodynamicist at NASA Langley Research center since 2006. Prior to that 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.