Shock structure in the 14 moment system of extended thermodynamics with high order closure based on the maximum entropy principle

An analysis of the shock structure in the 14 moment system of extended thermodynamics with first, second and third order closure based on the maximum entropy principle (MEP) is presented, as a follow up of a recent investigation of the shock structure in the 13 moment system with first and second MEP-based closure. It is seen that when adopting higher order closures, the strength of the subshock that appears in the shock structure profile for large enough Mach numbers is remarkably reduced with respect to what is found with the first order closure, and the overall profile of the shock structure solution is in better agreement with experimental results

Shock structure in extended thermodynamics with second-order maximum entropy principle closure

An investigation on the features of the shock structure solution of the 13-moment system of extended thermodynamics with a second-order closure based on the maximum entropy principle is presented. The results are compared to those obtained by means of the traditional first-order closure and to those obtained in the framework of kinetic theory by solving the Boltzmann equation with a BGK model for the collision term. It is seen that when adopting a second-order closure, the strength of the subshock that appears in the shock structure profile for large enough Mach numbers is remarkably reduced with respect to what is found with the first-order closure, and the overall profile of the shock structure solution is in better agreement with the results obtained with the kinetic theory approach. The analysis is extended to the case of the 14-moment system of a polyatomic gas, and some preliminary results are presented also for this case

Corrigendum to "Modelling wildland fire propagation by tracking random fronts" published in Nat. Hazards Earth Syst. Sci., 14, 2249–2263, 2014

G. Pagnini1,2 and A. Mentrelli1,3 1BCAM – Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain 2Ikerbasque, Basque Foundation for Science, Alameda Urquijo 36-5, Plaza Bizkaia, 48011 Bilbao, Basque Country, Spain 3Department of Mathematics & Alma Mater Research Center on Applied Mathematics (AM)2, University of Bologna, via Saragozza 8, 40123 Bologna, Ital

Modelling and simulation of wildland fire in the framework of the level set method

Among the modelling approaches that have been proposed for the simulation of wildfire propagation, two have gained considerable attention in recent years: the one based on a reaction-diffusion equation, and the one based on the level set method. These two approaches, traditionally seen in competition, do actually lead to similar equation models when the level set method is modified taking into account random effects as those due to turbulent hot air transport and fire spotting phenomena. The connection between these two approaches is here discussed and the application of the modified level set method to test cases of practical interest is shown

Wildfire propagation modelling

Wildfires are a concrete problem with a strong impact on human life, property and the environment, because they cause disruption and are an important source of pollutants. Climate change and the legacy of poor management are responsible for wildfires increasing in occurrence and in extension of the burned area. Wildfires are a challenging task for research, mainly because of their multi-scale and multi-disciplinary nature. Wildfire propagation is studied in the literature by two alternative approaches: the reaction-diffusion equation and the front tracking level-set method. The solution of the reaction-diffusion equation is a smooth function with an infinite domain, while the level-set method generates a sharp function that is not zero inside a compact domain. However, these two approaches can indeed be considered complementary and reconciled. With this purpose we derive a method based on the idea to split the motion of the front into a drifting part and a fluctuating part. This splitting allows specific numerical and physical choices that can improve the models. In particular, the drifting part can be provided by chosen existing method (e.g. one based on the level-set method) and this permits the choice for the best drifting part. The fluctuating part is the result of a comprehensive statistical description of the physics of the system and includes the random effects, e.g., turbulent hot-air transport and fire-spotting. As a consequence, the fluctuating part can have a non-zero mean (for example, due to ember jump lengths), which means that the drifting part does not correspond to the average motion. This last fact distinguishes between the present splitting and the well-known Reynolds decomposition adopted in turbulence studies. Actually, the effective front emerges to be the weighted superposition of drifting fronts according to the probability density function of the fire-line displacement by random effects. The resulting effective process emerges to be governed by an evolution equation of the reaction-diffusion type. In this reconciled approach, the rate of spread of the fire keeps the same key and characterising role that is typical in the level-set approach. Moreover, the model emerges to be suitable for simulating effects due to turbulent convection, such as fire flank and backing fire, the faster fire spread being because of the actions by hot-air pre-heating and by ember landing, and also due to the fire overcoming a fire-break zone, which is a case not resolved by models based on the level-set method. A physical parametrization of fire-spotting is also proposed and numerical simulations are shown.PhD Grant "La Caixa 2014

On variable-order fractional linear viscoelasticity

We discuss a generalisation of fractional linear viscoelasticity based on Scarpi's approach to variable-order fractional calculus. After reviewing the general mathematical framework, we introduce the variable-order fractional Maxwell model as a simple example for our analysis. We then provide some physical considerations for the fractionalisation procedure and on the choice of the transition functions. Lastly, we compute the material functions for the considered model and evaluate them numerically for exponential-type and Mittag-Leffler-type order functions.Comment: 14 pages, 17 figure

Energy dissipation in viscoelastic Bessel media

We investigate the specific attenuation factor for the Bessel models of viscoelasticity. We find that the quality factor for this class can be expressed in terms of Kelvin functions and that its asymptotic behaviours confirm the analytical results found in previous studies for the rheological properties of these models

The Riemann problem for a hyperbolic model of incompressible fluids

The aim of the present paper is to investigate shock and rarefaction waves in a hyperbolic model of incompressible fluids. To this aim, we use the so-called extended-quasi-thermal-incompressible (EQTI) model, recently proposed by Gouin and Ruggeri (H. Gouin, T. Ruggeri, International Journal of Non-Linear Mechanics 47 (2012) 688\u2013693). In particular, we use as constitutive equation a variant of the well-known Boussinesq approximation in which the specific volume depends not only on the temperature but also on the pressure, leading to a hyperbolic system of differential equations. The limit case of ideal incompressibility, namely when the thermal expansion coefficient and the compressibility factor vanish, is also considered. The results show that the propagation of shock waves in an EQTI fluid is characterized by small jump in specific volume and temperature, even when the jump in pressure is relevant, and rarefaction waves originating from a general Riemann problem are characterized by a very steep profile. The knowledge of the loci of the states that can be connected to a given state by a shock wave or a rarefaction wave allows also to completely solve the Riemann problem. The obtained results are confirmed by means of numerical calculations

Asymptotic Behavior of Riemann with Structure Problem for Hyperbolic Dissipative Systems

We test for a 2 x 2 hyperbolic dissipative system, by numerical experiments, the cojecture according to which the solution of the Riemann problem and Riemann prblem with structure converge, for large time to a combination of schock structures (with or without subshocks) and rarefaction of the equilibrium subsytem

Asymptotic-Preserving Scheme for Highly Anisotropic Non-Linear Diffusion Equations

Heat transfer in magnetically confined plasmas is a process characterized by non-linear and extremely high anisotropic diffusion phenomena. Standard numerical methods, successfully employed in the numerical treatment of classical diffusion problems, are generally inefficient, or even prone to break down, when such high anisotropies come into play, leading thus to the need of new numerical techniques suitable for this kind of problems. In the present paper, the authors propose a numerical scheme based on an asymptotic-preserving (AP) reformulation of this non-linear evolution problem, generalizing the ideas introduced in a previous paper for the case of elliptic anisotropic problems [P. Degond, A. Lozinski, J. Narski, C. Negulescu, An asymptotic-preserving method for highly anisotropic elliptic equations based on a micro\u2013macro decomposition, J. Comput. Phys. 231 (7) (2012) 2724\u20132740]. The performances of the here proposed AP scheme are tested numerically; in particular it is shown that the scheme is capable to deal with problems characterized by a high degree of anisotropy, thus proving to be suitable for the study of anisotropic diffusion in magnetically confined plasmas