Linear Fourier and Iteration-Delay Analysis of a Computational Fluid Dynamics Problem During Execution

The basic equations for the Fourier error analysis are developed and then applied to the scalar conservation equation of a sample computational fluid dynamics (CFD) problem in which variables are continuously updated. The analysis helps explain basic features of numerical stability. When divergence and neutral stability are encountered, Fourier analysis provides insight into the emergence and location of the instability, but is not by itself found to be a sufficient indicator of the existence of numerical instability. Further analysis of central differencing cases is made using a variation on time-delay reconstruction, from chaos theory.