Numerical Solution of Flame Sheet Problems with and without Multigrid Methods

Flame sheet problems are on the natural route to the numerical solution of multidimensional ames, which, in turn, are important in many engineering applications. In order to model the ame structure more accurately, we use the vorticity-velocity formulation of the uid ow equations instead of the streamfunction-vorticity approach. The numerical solution of the resulting nonlinear coupled elliptic partial di erential equations involves a pseudo transient process and a steady state Newton iteration. Rather than working with dimensionless variables, we introduce scale factors that can yield signi cant 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, using either one way or correction schemes.