Numerical solution of flame sheet problems with and without multigrid methods

Craig C. Douglas

Department of Computer Science, Yale University and
IBM Research Division Thomas J. Watson Research Center

Alexandre Ern

Department of Mechanical Engineering, Yale University and
CERMICS, ENPC, La Courtine, 93067, Noisy-le-Grand, FRANCE


Flame sheet problems are on the natural route to the numerical solution of multidimensional flames, which, in turn, are important in many engineering applications. In order to model the flame structure more accurately, we use the vorticity-velocity formulation of the fluid flow equations instead of the streamfunction-vorticity approach. The numerical solution of the resulting nonlinear coupled elliptic partial differential equations involves a pseudo transient continuation process and a steady state Newton iteration. Rather than working with dimensionless variables, we introduce scale factors that can yield significant savings in the execution time. In this context, we also investigate the applicability and performance of several multigrid methods, focusing on nonlinear Damped Newton multigrid, either one way or correction schemes.