Date of Award

Fall 10-27-2021

Degree Type

Masters Thesis

Degree Name

Master of Science (MS)

School

Mathematics and Natural Sciences

Committee Chair

James Lambers

Committee Chair School

Mathematics and Natural Sciences

Committee Member 2

C. S. Chen

Committee Member 2 School

Mathematics and Natural Sciences

Committee Member 3

Haiyan Tian

Committee Member 3 School

Mathematics and Natural Sciences

Abstract

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.

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.

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.

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