Lattice Boltzmann Methods (LBMs) are relatively new and have not yet been widely applied to ground-water systems. LBMs are particularly attractive for numerical modeling of flow and solute transport in karst aquifers because they are able to: • Simulate inertial flows • Incorporate complex wall and conduit geometries • Solve adjacent Darcian and Navier-Stokes flow regimes • Solve the appropriat...

Reaction-diffusion-advection equations provide precise interpretations for many important phenomena in complex interactions between natural and artificial systems. This paper studies second-order semi-discretizations the numerical solution of reaction-diffusion-advection modeling quenching types singularities occurring numerous applications. Our investigations particularly focus at cases where ...

• Rigorous homogenization of parabolic problems in evolving micro-domains. Reaction-diffusion-advection equations with nonlinear boundary conditions. Strong two-scale compactness result Kolmogorov-Simon-type. We consider a reaction-diffusion-advection problem perforated medium, reactions the bulk and at microscopic boundary, slow diffusion scaling. The microstructure changes time; microstructur...

The causes and implications of the regional variations in the spread of the incipient agriculture in Europe remain poorly understood. We apply population dynamics models to study the dispersal of the Neolithic in Europe from a localized area in the Near East, solving the two-dimensional reaction-diffusion equation on a spherical surface. We focus on the role of major river paths and coastlines ...

There are three distinct processes that are predominant in models of flowing media with inter-acting components: advection, reaction, and diffusion. Collectively, these processes are typicallymodelled with partial differential equations (PDEs) known as advection-reaction-diffusion (ARD)equations.To solve most PDEs in practice, approximation methods known as numerical methods are...

Advection-diffusion equation and its related analytical solutions have gained wide applications in different areas. Compared with numerical solutions, the analytical solutions benefit from some advantages. As such, many analytical solutions have been presented for the advection-diffusion equation. The difference between these solutions is mainly in the type of boundary conditions, e.g. time pat...

In this paper we consider discontinuous Galerkin (DG) finite element approximations of a model scalar linear hyperbolic equation. We show that in order to ensure continuous stabilization of the method it suffices to add a jump-penalty-term to the discretized equation. In particular, the method does not require upwinding in the usual sense. For a specific value of the penalty parameter we recove...