Numerical Stability Analysis of the Discretized Advection-diffusion Equation on Non-uniform Grids.

The numerical stability of discretized advection-diffusion equations is investigated on non-uniform grids by an eigenvalue analysis method. Stability analysis quantitatively provide the stability domain for typical non-uniform grids and show that stability domains are narrower than those for a uniform grid. Furthermore, stability domains under coordinate transformation to a uniform grid are obtained. Numerical experiments on non-uniform grids using the advection-diffusion equation are performed to verify the stability domain obtained in this study. [ABSTRACT FROM AUTHOR]