Student Scholars Day

Something Old and Something New: An Assessment of Two Numerical Solution Techniques for a Parabolic Partial Differential Equation Arising in Turbulent Particle Transport

Kirkhof Center 2266

Turbulent particle transport is a biologically important physical process in stream ecosystems. One of the models employed in studying this process is called the Local Exchange Model (LEM), which is a second-order parabolic partial differential equation with boundary conditions at the water surface and stream bed. A widely used numerical method known as the Crank-Nicolson scheme was used to obtain numerical solutions of the LEM. Though this method is commonly claimed to be unconditionally stable, it produced spurious oscillations for many parameter values when applied to the LEM. These oscillations were caused by the boundary conditions, which are not considered in the usual proof of stability for Crank-Nicolson. A review of the recent literature uncovered a new numerical method called exponential fitting, which was specifically designed to avoid spurious oscillations. This method successfully eliminated the oscillation problem when applied to the LEM.