Related papers: A deformed derivative model for turbulent diffusio…
Evaporation of a deformable droplet under convection is investigated and the performance of the classical and Abramzon-Sirignano (A-S) models is evaluated. Using the Immersed Boundary/Front-Tracking (IB/FT) method, interface-resolved…
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
The present article proposes a diffuse interface model for compressible multicomponent flows with transport phenomena of mass, momentum and energy (i.e., mass diffusion, viscous dissipation and heat conduction). The model is reduced from…
Modeling of water and gas flow in low-permeability media is an important topic for a number of engineering such as exploitation of tight gas and disposal of high-level radioactive waste. It has been well documented in the literature that…
Diffusion coefficients are essential microphysics input for modeling white dwarf evolution, as they impact phase separation at crystallization and sedimentary heat sources. Present schemes for computing diffusion coefficients are accurate…
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
Condensible substances are nearly ubiquitous in planetary atmospheres. For the most familiar case-water vapor in Earth's present climate-the condensible gas is dilute, in the sense that its concentration is everywhere small relative to the…
The aim of the study is to compare the standard Maxwell-Stefan model of diffusion with the higher-order one recently derived. This higher-order model takes into account the influence of the complete pressure tensor. A numerical scheme is…
The present paper deals with the numerical solution of time-fractional advection-diffusion equations involving the Caputo derivative with source term by means of an unconditionally stable implicit finite difference method on quasi-uniform…
The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in various natural sciences. In view of the fact that, in contrast…
The estimate of coefficients of the Convection-Diffusion Equation (CDE) from experimental measurements belongs in the category of inverse problems, which are known to come with issues of ill-conditioning or singularity. Here we concentrate…
The Westervelt equation describes the propagation of pressure waves in continuous nonlinear and, eventually, diffusive media. The classical framework of this equation corresponds to fluid dynamics theory. This work seeks to connect this…
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…
In this paper, a novel Hermite radial basis function-based differential quadrature method (H-RBF-DQ) is presented. This new method is designed to treat derivative boundary conditions accurately. The developed method is very different from…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
Proper modeling of complex systems requires innovative mathematical tools. In this sense, we sought to use deformed or fractal derivatives for studying the dynamics of systems, particularly those, such as granular gases, in which the…
We propose a numerical algorithm for solving the atmospheric dispersion problem with elevated point sources and ground-level deposition. The problem is modelled by the 3D advection-diffusion equation with delta-distribution source terms, as…
In this paper, we approximate numerically the solution of Caputo-type advection-diffusion equations of the form $D_t^{\alpha} u(t,x) = a_1(x)u_{xx}(t,x) + a_2(x)u_x(t,x) + a_3u(t,x) + a_4(t,x)$, where $D_t^{\alpha} u$ denotes the Caputo…
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady…