Related papers: Wildfires Quasi-Implicit Alternative-Direction Sim…
We present an implicit-explicit (IMEX) scheme for semilinear wave equations with strong damping. By treating the nonlinear, nonstiff term explicitly and the linear, stiff part implicitly, we obtain a method which is not only unconditionally…
We consider a special type of fast reaction-diffusion systems in which the coefficients of the reaction terms of the two substances are much larger than those of the diffusion terms while the diffusive motion to the substrate is negligible.…
In this study, a novel semi-implicit second-order temporal scheme combined with the finite element method for space discretization is proposed to solve the coupled system of infiltration and solute transport in unsaturated porous media. The…
We implement and test the exact time integration method proposed by Townsend 2009 for gas cooling in cosmological hydrodynamic simulations. The errors using this time integrator for the internal energy are limited by the resolution of the…
We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…
Various flame tracking techniques are often used in hydrodynamic simulations. Their use is indispensable when resolving actual scale of the flame is impossible. We show that parameters defining "artificial flame" propagation found from…
Electric grid faults can cause catastrophic wildfires, particularly in regions with high winds and low humidity. In real-time operations, electric utilities are often left with few options for wildfire risk mitigation, leading to use of…
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…
In recent decades, the intensification of wildfire activity in western Canada has resulted in substantial socio-economic and environmental losses. Accurate wildfire risk prediction is hindered by the intrinsic stochasticity of ignition and…
A cellular automaton (CA)-based modeling approach to simulate wildfire spread, emphasizing its strengths in capturing complex fire dynamics and its integration with geographic information systems (GIS). The model introduces an enhanced…
This paper is concerned with the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic PDEs with Galerkin finite element approximations. In particular, we study the time-dependent nonlinear Joule…
Solid fuel ignition models, for which the dynamics of the temperature is independent of the single-species mass fraction, attempt to follow the dynamics of an explosive event. Such models may take the form of singular, degenerate,…
In this article we propose and numerically implement a mathematical model for the simulation of three-dimensional semiconductor devices characterized by an heterogeneous material structure. The model consists of a system of nonlinearly…
The focus of this paper is on operating the electric power grid in a secure manner when wildfire risks are high. This is a challenging problem because of the uncertain ways in which the fires can impact the operation of the power system. To…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
Wildfire is an important system process of the earth that occurs across a wide range of spatial and temporal scales. A variety of methods have been used to predict wildfire phenomena during the past century to better our understanding of…
The calculation of thermal conductivity in insulating solids at temperatures below the Debye temperature is problematic, due to the breakdown of classical and semi-classical approaches. In this work, we present a fully quantum methodology…
Over 8,024 wildfire incidents have been documented in 2024 alone, affecting thousands of fatalities and significant damage to infrastructure and ecosystems. Wildfires in the United States have inflicted devastating losses. Wildfires are…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
We present a study of numerical behavior of a thickened flame used in Flame Capturing (FC, Khokhlov (1995)) for tracking thin unresolved physical flames in deflagration simulations. We develop a steady-state procedure for calibrating the…