Date of Award
Master of Science (MS)
Mechanical & Aerospace Engineering
Gene J. Hou
Miltiadis D. Kotinis
Duc T. Nguyen
The hypothesis of this research is that exponential interpolation functions will approximate fluid properties at shock waves with less error than polynomial interpolation functions. Exponential interpolation functions are derived for the purpose of modeling sharp gradients. General equations for conservation of mass, momentum, and energy for an inviscid flow of a perfect gas are converted to finite element equations using the least-squares method. Boundary conditions and a mesh adaptation scheme are also presented. An oblique shock reflection problem is used as a benchmark to determine whether or not exponential interpolation provides any advantages over Lagrange polynomial interpolation. Using exponential interpolation in elements downstream of a shock and having edges coincident with the shock showed a slight reduction in the solution error. However there was very little qualitative difference between solutions using polynomial and exponential interpolation. Regardless of the type of interpolation used, the shocks were smeared and oscillations were present both upstream and downstream of the shock waves. When a mesh adaptation scheme was implemented, exponential elements adjacent to the shock waves became much smaller and the numerical solution diverged. Changing the exponential elements to polynomial elements yielded a convergent solution. There appears to be no significant advantage to using exponential interpolation in comparison to Lagrange polynomial interpolation.
Smith, Bradford S.. "Modeling Shock Waves Using Exponential Interpolation Functions with the Least-Squares Finite Element Method" (2016). Master of Science (MS), thesis, Mechanical & Aerospace Engineering, Old Dominion University, https://digitalcommons.odu.edu/mae_etds/7