Luis Ferragut

An improved derefinement algorithm of nested meshes

Abstract In this paper we present a new version of the derefinement algorithm developed by Plaza et al . (in Numerical Methods in Engineering , Elsevier Science, Amsterdam, 1992, pp. 225–232; in Algorithms, Software, Architecture , Elsevier Science, Amsterdam, 1992, pp. 409–415; A. Plaza, PhD thesis, University of Las Palmas de Gran Canaria, 1993; Commun. Numer. Meth. Engng. , 1994, 10 , 403–412). 1–4 The purpose is to achieve a better derefinement algorithm with a lesser degree of complexity. We present the theoretical study of this improved derefinement algorithm and of the inverse one for refinement. Firstly, our initial version of the derefinement algorithm is summarized. Then we present the refinement algorithm associated with the improved derefinement one. Finally, automatic control of the sequences of irregular nested triangulations is shown by means of the resolution of an unsteady problem. In this problem the initial mesh has only nine nodes and a combination of refinements and derefinements have been applied to approach both the circular domain and the initial solution.

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.

The Evolution of a WILDLAND Forest FIRE FRONT

The rate of the spread and shape of a forest fire front is a problem that has not been thoughtfully studied from a computer graphics perspective. Here, using physically based computer graphics modeling, we propose a model for the simulation of wildland fires over 3D complex terrain. The model is based on conservation laws of energy and species, which includes radiation convection, reaction and natural convection, and takes into account the endothermic and exothermic phases of this kind of phenomenon. As an application, a simulation of a wildland fire in the Ebro basin of Spain is presented. The results are visualized on synthetic imagery, obtained by using the digital model of the studied terrain plus its corresponding images acquired by the Spot 4 and LandSat TM satellites.

APPLICATION OF A NONLINEAR EVOLUTION MODEL TO FIRE PROPAGATION

The numerical simulation of fire in forest has been an important objective in recent researches, The rate of spread and shape of a forest fire front is af8ecte.d by many factors. The most important of these are as follows: fuel type and moisture content, wind velocity and variability, forest topography, fire spread mechanism, fuel continuity and the amount of spotting (cf.[ l-21). The development of Geographic Information Systems allows the incorporation of these data to the developed models, The first models took into account constant factors, continuous uniform fuel type, constant wind velocity, moisture and slope. Under these conditions, a fire ignited at a single point reaches a quasi-steady state and progresses toward the down wind direction and expands at a constant rate. These data cannot give precise predictions under variable conditions but are very useful in order to the intuition of the fire controller. Models capable of being incorporated into the computer simulations of fires under variable conditions have been developed, based on cellular automata (cf. [3-7]), and stochastic process [8]. These models can give useful indicators as to fire behavior under such conditions. Combustion phenomena has been extensively studied [9], unsteady flame propagation has been analyzed [lo]. Models based on combustion theories are very difficult to develop because of the diversity of the fuel type and varied chemical composition within a given fuel type. Because of the complexity of the problem, models based rigorously on combustion theory have not been completely developed. In this preliminary work, a first attempt is done to design a computer code for numerical simulation of forest fire spread in landscapes. Basically a convection-diffusion model for temperature and a mass-consistent model for wind field simulation will be assumed. A two-steps chemical mechanism is simplified in order to obtain the heat source. This proposed 2-D model take into account the convection phenomena due to temperature gradients in vertical direction. A numerical solution of the former model is presented using a finite difference method together with the study of stability. This numerical method is contrasted with an adaptive finite element method using reflnementiderefinement techniques (cf. [ 1 1 - 143).

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.

Solution of linear systems from an optimal control problem arising in wind simulation

Several solution strategies for a class of large, sparse linear systems with a block 2 × 2 structure arising from the finite element discretization of an optimal control problem in wind simulation are introduced and analyzed. Block preconditioners and a sparse direct solver on the original coupled system are compared with a preconditioned GMRES iteration applied to a reduced system (Schur complement). Theoretical and experimental results demonstrate the effectiveness of the reduced system approach. Copyright

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 Numerical Adaptive Algorithm for the Obstacle Problem

This paper concerns an adaptive finite element method for the elliptic obstacle problem. We consider the formulation of the problem as an elliptic variational inequation. The adaptive algorithm (modified Uzawa adaptive method)we construct is based on a combination of the Uzawa method associated with the corresponding multivalued operator and a convergent adaptive method for the linear problem. As our main result we show that if the adaptive method for the linear problem is convergent, then the adaptive modified Uzawa method is convergent as well. A numerical experiment shows the studied properties of the method.