Coupled atmospheric-fire modeling employing the method of averages

A conservative forward-in-time numerical technique to improve the efficienc y of a fully compressible wildfire model is presented. The technique is bas ed on a method of averaging (MOA), which allows the costly advective terms based on a synchronous advection algorithm (e.g., the monotonicity of scala r fields is preserved) to be computed on a time step several rimes larger t han would be dictated by the speed of the fastest waves. The MOA technique is explicit and does not require the use of either direct or iterative solv ers to invert a matrix; instead the governing equations are solved to first order within an inner loop in which time-averaged quantities are obtained for use in a more costly outer loop. A linearized stability analysis of the entire scheme, including the interaction of gravity wave propagation and m aterial motion, is presented and numerical stability for a wide range of ph ysical and numerical parameters is demonstrated. Convergence studies are us ed to verify that the overall method maintains second-order accuracy. A mod el to simulate the propagation of the firefront in wildfires is described, and several calculations are provided to illustrate the application and adv antages of the MOA in a problem that includes many complex physical process es.