Explicit Von Neumann Stability Conditions for the C-Tau Scheme: A Basic Scheme in the Development of the Ce-Se Courant Number Insensitive Schemes

As part of the continuous development of the space-time conservation element and solution element (CE-SE) method, recently a set of so called “Courant number insensitive schemes” has been proposed. The key advantage of these new schemes is that the numerical dissipation associated with them generally does not increase as the Courant number decreases. As such, they can be applied to problems with large Courant number disparities (such as what commonly occurs in Navier-Stokes problems) without incurring excessive numerical dissipation. A basic scheme in the development of the Courant number insensitive schemes is the so called “c-τ scheme”. It is a solver of the PDE ∂u ∂t + a ∂u ∂x =0 where a �= 0 is a constant. At each space-time staggered mesh points (j, n), the c-τ scheme is formed by u n = 1 �