Joseph Johnson is a third year student at the University of Melbourne. He is studying Applied Mathematics and majoring in Mathematical Physics.
He plans to undertake a Masters in Applied Mathematics in 2016 at the University of Melbourne and continue his research into numerical solutions to the Boltzmann equation.
When he was a small child walking with his parents along Royal Parade they passed the University of Melbourne and he asked what this castle was. They told him that this was a place where people got paid to think about things and search for answers to the world’s toughest problems. He decided that he wanted to solve problems and he would work in that castle one day.
Joseph is especially indebted to his mother for the persistence and aptitude for mathematics that has brought him here. As an undergraduate he has enjoyed studying the mathematical models that attempt to patch together our understanding of nature. Mathematical modeling has become his main interest and he will pursue it as long as it continues to amaze and challenge him.
Joseph’s other interests have included tennis, soccer, Australian Rules football, crossfit and American football. Currently he enjoys weightlifting and running.
Numerical Solution Of The Boltzmann Equation For Rarefied Gas Flows
Numerical methods for solving the Boltzmann equation at arbitrary degrees of gas rarefied are critical to a range of technologies, including modern advances in nanoeletromechanical systems. This project will investigate a new approach to numerically solving the Boltzmann equation for rarefied gas flows. This method solves a simplified equation that removes dependence of the degree of rarefaction, as specified by the Knudsen number, which is then incorporated into the full solution using standard numerical methods. The promise is highly efficient numerical solutions at arbitrary degrees of rarefaction. Numerical investigation will verify this.