Project Team
Students
Timmy Susai Rajan
Computer Engineering, Mathematics
Penn State Abington, Penn State University Park
Faculty Mentors
Faranak Pahlevani
Penn State Abington
Division of Science and Engineering
Corina Drapaca
Penn State University Park
Department of Engineering Science and Mechanics
Lisa G. Davis
Montana State University
Department of Mathematical Sciences
Project
https://sites.psu.edu/mcreu/files/formidable/2/MC-REU-2022.pdf
Project Video
Project Abstract
The focus of this research is to develop an accurate numerical scheme for linear hyperbolic equations. This work is motivated by the mathematical model of DNA transcription using classic traffic flow models considering a constant elongation velocity along the gene. The numerical treatments for model simulations include adding a time filter to the classical upwind scheme for increased accuracy with a nominal computational cost. The filtered schemes are studied and analyzed using two methods of constant and adaptive time steps. Numerical computations illustrate stability and convergence of the filtered schemes in either case. An optimal filter parameter value was determined for when a constant time step is employed. The adaptive time step algorithm with the right choice of relevant parameters for classical upwind shows an improved accuracy compared to that of the best-performing filtered scheme.
Evaluate this Project
Use this form link to provide feedback to the presenters, and add your project evaluation for award(s) consideration.