Numerical Solutions of BVPs in 2-D Viscous Compressible Flows Using hpk Framework

Abstract

This paper presents numerical simulations of the two dimensional boundary value problems (BVPs) in viscous compressible flows using finite element method in hpk framework [1]–[2] in which the integral forms are variationally consistent (VC). The mathematical models utilize Navier-Stokes equations incorporating physical viscosity, conductivity and other transport properties. The finite element method based on hpk framework permits higher order global differentiability approximation and the variationally consistent integral forms [1]–[2] ensure unconditionally stable computations for all choices hpk and the dimensionless parameters in the mathematical models and thus do not require the use of upwinding methods such as SUPG/DC/LS [3]–[4]. Mach 1, 2, 3 and 5 flows over a flat plate (Carter's plate) is used as a model problems with ideal gas law.

Keywords:

• 2-D Compressible Flow
• Carter's Plate
• hpk Framework
• Navier-Stokes Equations
• Variational Consistency

This work has been supported by the DEPSCoR/AFOSR and AFOSR under grant numbers F49620-03-1-0298 and F49620-03-1-0201 to the University of Kansas, Department of Mechanical Engineering and Texas A&M University Department of Mechanical Engineering. The seed grant from ARO under the grant number FED46680 is gratefully acknowledged. The financial support provided by the second and the fourth authors' endowed professorships is gratefully acknowledged. The fellowships provided by the School of Engineering and the Mechanical Engineering Department of the University of Kansas are also acknowledged. The computational facilities for this work have been provided by the Computational Mechanics Laboratory (CML) of the University of Kansas, Department of Mechanical Engineering.