High-order numerical diffusion is commonly used in numerical models to provide scale selective control over small-scale noise. Conventional high-order schemes have undesirable side effects, however: they can introduce noise themselves. Two types of monotonic high-order diffusion schemes are proposed. One is based on flux correction/limiting on the corrective fluxes, which is the difference betw...

We present a numerical method for computing diffusive transport on a surface derived from image data. Our underlying discretization method uses a Cartesian grid embedded boundary method for computing the volume transport in a region consisting of all points a small distance from the surface. We obtain a representation of this region from image data by using a front propagation computation based...

In this paper, the authors consider the first boundary value problem for the nonlinear reaction diffusion equation: ut −∆um = αup1 in Ω, a smooth bounded domain in Rd(d ≥ 1) with the zero lateral boundary condition and with a positive initial condition, m ∈ ]0, 1[ (fast diffusion problem), α ≥ 0 and p1 ≥ m. Sufficient conditions on the initial data are obtained for the solution to vanish or bec...

[1] Physics‐based global magnetosphere modeling requires large computational resources. It is still impractical to resolve the computational domain to the point where numerical errors become negligible. One possible way of reducing numerical diffusion is the “Boris correction”: the semirelativistic magnetohydrodynamics equations are solved with an artificially reduced speed of light. Here we in...

We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer–Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent ‘eddy diffusion’. W...

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 transport of individual phases. Moreover, for compressible media, the pressure equation itself is just a time-dependent convection-diffusion equation. For differen...

The aim of this work is to find efficient and reliable numerical solutions of two complex problems under consideration. In the first application problem, an improved continuum model has been derived to describe the temperature and concentration distributions in gas-solid-fluidized beds with spray injection. The model equations for the nozzle spray are also reformulated to achieve reliable numer...

Within biological systems, which contain complex and composite media, diffusion may depend not only on internal geometry, but also on the chemical interactions between solid phase and transported particles. New hierarchical multiscale microstructural model for diffusion within complex media is presented. Hierarchical modeling approach is then employed to construct a continuum diffusion model ba...

In this paper, we propose an algorithm for numerical solving an inverse nonlinear diffusion problem. The algorithm is based on the linearized nonlinear terms by Taylor ́s series expansion, removed the time-dependent terms by Laplace transform, and so, the results at a specific time can be calculated without step-by-step computations in the time domain. Finite difference technique used for discre...