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In this contribution, I give an overview of the various approaches toward the numerical modelling of turbulence, particularly, in the interstellar medium. The discussion is placed in a physical context, i. e. computational problems are…
The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three…
In the sequel, we extend our previous work on the Minkowski Curve to Sierpi\'{n}ski simplices (Gasket and Tetrahedron), in the case of the heat equation. First, we build the finite difference scheme. Then, we give a theoretical study of the…
We present a mechanism for thermalizing a moving particle by microscopic deterministic scattering. As an example, we consider the periodic Lorentz gas. We modify the collision rules by including energy transfer between particle and…
In this paper, we present a Newton-like method based on model reduction techniques, which can be used in implicit numerical methods for approximating the solution to ordinary differential equations. In each iteration, the Newton-like method…
The role of thermal relaxation in nanoparticle melting is studied using a mathematical model based on the Maxwell--Cattaneo equation for heat conduction. The model is formulated in terms of a two-phase Stefan problem. We consider the cases…
A reaction-diffusion problem with a Caputo time derivative is considered. An integral discretization scheme on a graded mesh along with a decomposition of the exact solution is proposed. The truncation error estimate of the discretization…
Convergence results are stated for the variational iteration method applied to solve an initial value problem for a system of ordinary differential equations.
We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given…
To faithfully simulate ITER and other modern fusion devices, one must resolve electron and ion fluctuation scales in a five-dimensional phase space and time. Simultaneously, one must account for the interaction of this turbulence with the…
Using the test-particle method, we solve numerically the Boltzmann equation for an ultra-cold gas of trapped fermions with realistic particle number and trap geometry in the normal phase. We include a mean-field potential and in-medium…
In this paper, diffusion in polymer solutions undergoing evaporation of solvent is modeled as a coupled heat and mass transfer problem with moving boundary condition within the framework of nonequilibrium thermodynamics. The proposed…
We use a simple gas model to study non-equilibrium aspects of the multiparticle dynamics relevant to heavy ion collisions. By performing numerical simulations for various initial conditions we identify several characteristic features of the…
In this paper, we solve Laplace equation analytically by using differential transform method. For this purpose, we consider four models with two Dirichlet and two Neumann boundary conditions and obtain the corresponding exact solutions. The…
We formulate a numerical method to solve the porous medium type equation with fractional diffusion \[ \frac{\partial u}{\partial t}+(-\Delta)^{\sigma/2} (u^m)=0 \] posed for $x\in \mathbb{R}^N$, $t>0$, with $m\geq 1$, $\sigma \in (0,2)$,…
We describe a technique to derive constraints on the differential emission measure (DEM) distribution, a measure of the temperature distribution, of collisionally ionized hot plasmas from their X-ray emission line spectra. This technique…
We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…
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…
Ternary fission probabilities for thermal neutron induced fission of plutonium are analyzed within the framework of an evaporation-based model where the complexity of time-varying potentials, associated with the neck collapse, are included…
When the Vlasov equation is investigated numerically using the method of test particles, the particle-particle interactions that inevitably arise in the simulation (but are not present in the Vlasov equation itself) result in an…