New numerical approaches for coupled atmosphere-fire models

The rapid increase in computing power over the past few years have made possible the development of coupled atmosphere-fire models. In conjunction with the development of these models questions have been raised with respect to what approximations, if any, can be made in both the analytical and the numerical representation of the equations governing atmospheric flow near wildfires. In the past numerical weather prediction models applied to typical atmospheric flow situations have employed simplifications in which sound waves have been either eliminated or split from the models. The splitting or removal of sound waves allowed these models to be run at time steps much larger than dictated by the speed of sound. Unfortunately, the assumptions used in these models regarding the removal or elimination of sound waves may not be appropriate for the accurate simulation of wildfires. At Los Alamos, we have developed an atmospheric model, HIGRAD, in which sound waves are neither split nor eliminated; however, HIGRAD still employs numerical techniques, the method-of-averaging (MOA) approach and the Newton-Krylov approach, for which the time step of the model is not governed by the speed of sound. In principle, the MOA approach can be viewed as an explicit approach in which the effects of sound waves are, as the name implies, averaged---in such a way to ensure stability of the model. Also, the MOA approach is unlike other traditional explicit splitting approaches in that the method is fully second-order in time and space and can readily incorporate rather complex numerical schemes. HIGRAD's other flow solver, the Newton-Krylov approach, can in principle solve the entire Navier-Stokes equation set implicitly...including all nonlinear terms. The mechanics of this approach have only recently been developed at Los Alamos, but application of this solver on various fluid dynamical problems have revealed the importance of incorporating nonlinearities with respect to solution convergence. An important aspect of the nonlinear Newton-Krylov solver is that the functionals in place within the solver can be linearized to solve systems of equations employed in, for example, anelastic models. Thus, with only simple changes to the solver, the effect of neglecting temporal changes in density or sound waves can be investigated. We intend to show results from wildfire simulations employing this solver under varying levels of simplifications, as well we plan to compare the Newton-Krylov approach against the MOA approach with respect to the simulation of wildfires.