M.I. Asensio

A numerical method for solving convection-reaction-diffusion multivalued equations in fire spread modelling

A numerical method is developed for fire spread simulation modelling. The two-dimensional surface model presented takes into account moisture content, radiation, wind and slope effects, which are by far the most important mechanisms in fire spread. We consider the combustion of a porous solid, where the energy conservation equation is applied. The influence of moisture content and eventually heat absorbtion by pyrolysis, can be represented as two free boundaries, and are treated here using a multivalued operator representing the enthalpy. The maximal monotone property of this operator allows the implementation of a numerical algorithm with good convergence properties.

Space-Time adaptive algorithm for the mixed parabolic problem

In this paper we present an a-posteriori error estimator for the mixed formulation of a linear parabolic problem, used for designing an efficient adaptive algorithm. Our space-time discretization consists of lowest order Raviart-Thomas finite element over graded meshes and discontinuous Galerkin method with variable time step. Finally, several examples show that the proposed method is efficient and reliable.

Sensitivity analysis and parameter adjustment in a simplified physical wildland fire model

A simplified physical 2D wildland fire model is summarized.Some aspects of the numerical techniques used to solve the model are outlined.The simplicity of the model and the numerical techniques proposed allow very competitive computational times.The model is applied to a well measured experimental example.A global sensitivity analysis of the model is performed in order to validate the simplications proposed.A parameter adjustment of the model applied to the experimental example is carried out. A global sensitivity analysis and parameter adjustment of a simplified physical fire model applied to a well measured experimental example is developed in order to validate the model. The fire model is a simplified physical 2D wildland fire model with some 3D effects that takes into account the wind, the slope of the orography, the fuel load and type, the moisture content, the energy lost in the vertical direction and the radiation from the flames. The simplicity of the model and the numerical techniques proposed allow very competitive computational times.

A Wildland Fire Physical Model Well Suited to Data Assimilation

In this article, we focus on a simplified two-dimensional fire model with some three-dimensional effects. The model takes into account the moisture content and the energy lost in the vertical direction and to radiation from the flames. We couple this model with a local wind model, well adapted to fire modelling. The topography, fuel type, mass fraction of the fuel and the meteorological data required by the model (temperature, humidity and wind) are provided by geographic information systems. We incorporate data assimilation techniques to our fire model in order to improve the approximations obtained with the model. The data assimilated are the temperature of the solid fuel (which is related to the position of the fire front) and the mass fraction of fuel at certain points in the domain. The numerical examples show that this procedure is able to correct the approximations obtained by the model simulations, providing more realistic predictions. The process is implemented using parallel computing.

Numerical methods for modelling leaching of pollutants in soils

Linear equilibrium and non-equilibrium models for leaching of solutes in soils give rise to unsteady linear convection-diffusion-reaction problems. We present several numerical schemes to approximate the solution of this kind of problems based on Stabilized Finite Element Methods, including the recent Link-Cutting Bubbles strategy adapted to deal with unsteady problems, which gives the best numerical results.

A Simplified Wildland Fire Model Applied to a Real Case

We present a simplified 2D wildland fire model with some 3D effects, which takes into account convection and radiation. The topography, the fuel load and type and the meteorological data required by the model (temperature, humidity and wind) are provided via GIS. The wind conditions can be considered a given data in all domain, or can be computed by the wind model developed by authors. Given the fire ignition location and time the model provide the state of landscape for several time steps, allowing to establish the perimeter of the fire at different instants. By modifying the fuel load and type raster files, fire suppression tactics can be incorporated in order to adapt the simulation to the real situation, since the simplified model and its numerical solution allow a computational time much less than real time.

An efficient algorithm for solving a multi-layer convection-diffusion problem applied to air pollution problems

An urban scale Eulerian non-reactive multilayer air pollution model is proposed describing convection, turbulent diffusion and emission. A mass-consistent wind field model developed by authors is included in the air pollution model. An Adaptive Finite Element Method with characteristics in the horizontal directions and Finite Differences in the vertical direction using splitting techniques is proposed to numerically solve the corresponding PDE problem. A parallel version of the algorithm improves the precision of the solution keeping computation time below real time of simulation. A numerical example illustrates the whole problem.

Time-Space & Space-Time Elements for Unsteady Advection-Dominated Problems

The numerical simulation of advection-diffusion problems has been a subject of active research during the last thirty years. In this paper we look at the unsteady problem. Following with the research initiated in [4], our aim is to study the issue of how some of the stabilization techniques proposed for the steady problem could be appropriately combined and used with time integration Discontinuous Galerkin (DG) methods, so that the resulting fully discretized scheme is able to capture and reproduce the small scales into the coarse ones. Our starting point is based on the simple observation that in the non-stationary problem we have two types of partial differentiation which might be considered of different nature: the spatial convection-diffusionreaction operator and the time derivative which determines the evolution of the convection-diffusion-reaction processes. Therefore, at the very first step of designing the numerical method, two rather different strategies arise:

Parallel Implementation of a Simplified Semi-physical Wildland Fire Spread Model Using OpenMP

We present a parallel 2D version of a simplified semi-physical wildland fire spread model based on conservation equations, with convection and radiation as the main heat transfer mechanisms. This version includes some 3D effects. The OpenMP framework allows distributing the prediction operations among the available threads in a multicore architecture, thereby reducing the computational time and obtaining the prediction results much more quickly. The results from the experiments using data from a real fire in Galicia (Spain) confirm the benefits of using the parallel version.

A-Posteriori Error Analysis of a Mixed Method for Linear Parabolic Problem

In this paper we present a-posteriori error estimator for the mixed formulation of linear parabolic problem, and we use them in designing an efficient adaptive algorithm. Our space-time discretization consist of lowest order Raviart-Thomas finite element over graded meshes, and discontinuous Galerkin method with varying time-steps.