Multi-valued Solutions for the Equation of Motion, Darcy-Jordan Model, as a Cauchy Problem: A Shocking Event

<p>Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.</p> <p>The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial conditions.</p> <p>The approach taken in this study is the development of a hybrid algorithm combining the reliability of the Bisection Method and the efficiency of the Secant method. The developed algorithm is coded in MATLAB.</p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Masters Thesis

Year dc:date.available

2021

Author dc:creator

• Shimp, Chandler

Contributors dc:contributor

• James Lambers
• C. S. Chen
• Haiyan Tian

• Shock waves
• Equation of Motion
• Darcy-Jordan Model
• Poroacoustics
• Numerical Analysis
• Numerical Analysis and Computation
• Other Applied Mathematics
• Partial Differential Equations
• Theory and Algorithms

Repository record dc:identifier

https://aquila.usm.edu/masters_theses/866

OAI identifier oai:identifier

oai:aquila.usm.edu:masters_theses-1929