scholarly journals Implicit-Explicit Methods for a Convection-Diffusion-Reaction Model of the Propagation of Forest Fires

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1034 ◽  
Author(s):  
Raimund Bürger ◽  
Elvis Gavilán ◽  
Daniel Inzunza ◽  
Pep Mulet ◽  
Luis Miguel Villada
Keyword(s):  
Forest Fires ◽  
Control Strategies ◽  
Reaction Diffusion ◽  
Reaction Model ◽  
Diffusion Reaction ◽  
Nonlinear Convection ◽  
Splitting Technique ◽  
Convection Diffusion ◽  
Fuel Density ◽  
Diffusion Convection

Numerical techniques for approximate solution of a system of reaction-diffusion-convection partial differential equations modeling the evolution of temperature and fuel density in a wildfire are proposed. These schemes combine linearly implicit-explicit Runge–Kutta (IMEX-RK) methods and Strang-type splitting technique to adequately handle the non-linear parabolic term and the stiffness in the reactive part. Weighted essentially non-oscillatory (WENO) reconstructions are applied to the discretization of the nonlinear convection term. Examples are focused on the applicative problem of determining the width of a firebreak to prevent the propagation of forest fires. Results illustrate that the model and numerical scheme provide an effective tool for defining that width and the parameters for control strategies of wildland fires.

scholarly journals A 2D Convection-Diffusion Model of Anodic Oxidation of Organic Compounds Mediated by Hydroxyl Radicals Using Porous Reactive Electrochemical Membrane

Membranes ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 102 ◽  
Author(s):  
Ekaterina Skolotneva ◽  
Clement Trellu ◽  
Marc Cretin ◽  
Semyon Mareev
Keyword(s):  
Organic Compounds ◽  
Hydroxyl Radicals ◽  
Current Density ◽  
Current Density Distribution ◽  
Reaction Model ◽  
Diffusion Reaction ◽  
Unknown Parameters ◽  
Distribution Profile ◽  
Convection Diffusion ◽  
Oxidation Of Organic Compounds

In recent years, electrochemical methods utilizing reactive electrochemical membranes (REM) have been considered as a promising technology for efficient degradation and mineralization of organic compounds in natural, industrial and municipal wastewaters. In this paper, we propose a two-dimensional (2D) convection-diffusion-reaction model concerning the transport and reaction of organic species with hydroxyl radicals generated at a TiOx REM operated in flow-through mode. It allows the determination of unknown parameters of the system by treatment of experimental data and predicts the behavior of the electrolysis setup. There is a good agreement in the calculated and experimental degradation rate of a model pollutant at different permeate fluxes and current densities. The model also provides an understanding of the current density distribution over an electrically heterogeneous surface and its effect on the distribution profile of hydroxyl radicals and diluted species. It was shown that the percentage of the removal of paracetamol increases with decreasing the pore radius and/or increasing the porosity. The effect becomes more pronounced as the current density increases. The model highlights how convection, diffusion and reaction limitations have to be taken into consideration for understanding the effectiveness of the process.

scholarly journals A Numerical Handling of the Boundary Conditions Imposed by the Skull on an Inhomogeneous Diffusion-Reaction Model of Glioblastoma Invasion Into the Brain: Clinical Validation Aspects

2017 ◽  
Vol 16 ◽  
pp. 117693511668482
Author(s):  
Georgios S Stamatakos ◽  
Stavroula G Giatili
Keyword(s):  
Boundary Conditions ◽  
In Silico ◽  
Doubling Time ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Reaction Model ◽  
Diffusion Reaction ◽  
Clinical Validation ◽  
Imaging Data ◽  
Case Scenario

A novel explicit triscale reaction-diffusion numerical model of glioblastoma multiforme tumor growth is presented. The model incorporates the handling of Neumann boundary conditions imposed by the cranium and takes into account both the inhomogeneous nature of human brain and the complexity of the skull geometry. The finite-difference time-domain method is adopted. To demonstrate the workflow of a possible clinical validation procedure, a clinical case/scenario is addressed. A good agreement of the in silico calculated value of the doubling time (ie, the time for tumor volume to double) with the value of the same quantity based on tomographic imaging data has been observed. A theoretical exploration suggests that a rough but still quite informative value of the doubling time may be calculated based on a homogeneous brain model. The model could serve as the main component of a continuous mathematics-based glioblastoma oncosimulator aiming at supporting the clinician in the optimal patient-individualized design of treatment using the patient’s multiscale data and experimenting in silico (ie, on the computer).

scholarly journals First steps towards a dynamical model for forest fire behaviour in Argentinian landscapes

2020 ◽  
Vol 20 (2) ◽  
pp. e09
Author(s):  
Monica Denham ◽  
Karina Laneri ◽  
Viviana Zimmerman ◽  
Sigfrido Waidelich
Keyword(s):  
Forest Fire ◽  
Forest Fires ◽  
Reaction Diffusion ◽  
Dynamical Model ◽  
Weather Index ◽  
Fire Weather Index ◽  
Fire Propagation ◽  
Diffusion Convection ◽  
And Diffusion ◽  
Simulation Time

We developed a Reaction Diffusion Convection (RDC) model for forest fire propagation coupled to a visualization platform with several functionalities requested by local firefighters. The dynamical model aims to understand the key mechanisms driving fire propagation in the Patagonian region. We'll show in this work the first tests considering combustion and diffusion in artificial landscapes. The simulator, developed in CUDA/OpenGL, integrates several layers including topography, weather, and fuel data. It allows to visualize the fire propagation and also to interact with the user in simulation time. The Fire Weather Index (FWI), extensively used in Argentina to support operative preventive measures for forest fires management, was also coupled to our visualization platform. This additional functionality allows the user to visualize on the landscape the fire risks, that are closely related to FWI, for Northwest Patagonian forests in Argentina.

Optimization analysis of the inverse coefficient problem for the nonlinear convection-diffusion-reaction equation

2018 ◽  
Vol 26 (6) ◽  
pp. 821-833 ◽  
Author(s):  
Roman V. Brizitskii ◽  
Zhanna Y. Saritskaya
Keyword(s):  
Boundary Value ◽  
Diffusion Reaction ◽  
Stability Estimates ◽  
Coefficient Problem ◽  
Reaction Equation ◽  
Nonlinear Convection ◽  
Inverse Coefficient Problem ◽  
Convection Diffusion ◽  
Reaction Coefficient ◽  
Inverse Coefficient

AbstractThe inverse coefficient problem for the nonlinear convection-diffusion-reaction equation is considered. A velocity vector and a mass-transfer coefficient are considered as the unknown coefficients and are recovered with the help of the additional information about the boundary value problem’s solution. The inverse coefficient problem is reduced to a two-parameter problem of multiplicative control, the solvability of which is proved in a general form. For a cubic reaction coefficient the local stability estimates of the control problem’s solutions are obtained regarding to a rather small perturbation of either the cost functional or the specified functions of the boundary value problem.

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