A Simulation Study of Central Schemes for Solving One Dimensional Hyperbolic Problems

Undergraduate #246
Discipline: Computer Sciences and Information Management
Subcategory:

Denzel White - Central State University
Co-Author(s): Damon Harper and Justice Mullins, Central State University, Wilberforce, OH

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We need to solve hyperbolic problems in many science and engineering applications, such as flows through porous media and magneto-hydrodynamics. In solving such hyperbolic problems, high-resolution, non-oscillatory central schemes are efficient. The Lax-Friedrichs (LxF) scheme is the forerunner of all central differencing. The authors in [Pereira and Rahunanthan, 2011] presented a second-order central scheme. This scheme is in a simple semi-discrete form. The semi-discrete scheme is then solved by an appropriate time advancing scheme. In this research we use the scheme to solve a set of one dimensional problems. Numerical simulations will be presented in support of the study.

Funder Acknowledgement(s): NSF HBCU-UP (Award Abstract No.: 1016283)

Faculty Advisor: Arunasalam Rahunanthan, aRahunanthan@centralstate.edu

Role: With my co-authors, I have been simulating simple one-dimensional hyperbolic problems, such as Burgers' equation.