Coupled Atmospheric–Fire Modeling Employing the Method of Averages

Abstract

A conservative forward-in-time numerical technique to improve the efficiency of a fully compressible wildfire model is presented. The technique is based on a method of averaging (MOA), which allows the costly advective terms based on a synchronous advection algorithm (e.g., the monotonicity of scalar fields is preserved) to be computed on a time step several times larger than 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 solvers 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 material motion, is presented and numerical stability for a wide range of physical and numerical parameters is demonstrated. Convergence studies are used to verify that the overall method maintains second-order accuracy. A model to simulate the propagation of the firefront in wildfires is described, and several calculations are provided to illustrate the application and advantages of the MOA in a problem that includes many complex physical processes.