An unconditionally stable method for air motion inside cylinders

Abstract

A mixed implicit semi Lagrangian finite difference‐finite volume method for numerical simulation of 2D air motion inside cylinders is derived and discussed. A conformal mapping from a physical (moving) domain to a computational (fixed) one is resorted in order to deal with a grid independent of time, making the numerical code very efficient. The numerical method is mass and energy conservative, unconditionally stable and at each timestep requires the solution of two well structured five‐band systems of linear equations. Its accuracy is first order in time and second one in space where the solution is smooth, while due to FCT space accuracy drops to the first order where the solution is steep. Stability of the method is proved both by a classical Von Newmann analysis and analysis of the matrices involved in the systems of linear equations. All these elements make the numerical method particularly fast. Numerical experiments are performed that show the influence of the maximum Courant number (with respect to the fluid speed) on the performance of the numerical method; moreover, comparison of simulations with a major existing code for engines is worked out.

Citation

Abrugia, G. and Amato, U. (1998), "An unconditionally stable method for air motion inside cylinders", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 8 No. 8, pp. 864-887. https://doi.org/10.1108/09615539810241105