We consider a system of coupled partial differential equations modeling the interaction of mussels and algae in advective environments. A key parameter in the equations is the ratio of the diffusion rate of the mussel species and the advection rate of the algal concentration. When advection dominates diffusion, one observes large-amplitude solutions representing bands of mussels propagating slo...

In this note we study advection-diffusion equations associated to incompressible $$W^{1,p}$$ velocity fields with $$p>2$$ . We present new estimates on the energy dissipation rate and discuss applications of upper bounds enhanced rate, lower $$L^2$$ norm density, quantitative vanishing viscosity estimates. The key tools employed in our argument are a propagation regularity result, coming from t...

A two-dimensional two-phase numerical model is developed to predict transport and fate of oil slicks which resulted the concentration distribution of oil on the water surface. Two dimensional governing equation of fluid flow which consists mass and momentum conservation was solved using the finite difference method on the structured staggered grid system. The resulted algebric equations were so...

In this paper, we propose to improve the stabilized POD-ROM introduced in [48] deal with numerical simulation of advection-dominated advection-diffusion-reaction equations. particular, a three-stage stabilizing strategy that will be very useful when considering low diffusion coefficients, i.e. strongly regime. This approach mainly consists three ingredients: (1) addition “streamline diffusion” ...

The characteristics of the hydro-thermal flow which occurs when a cold fluid is injected into a hot fractured bedrock depend on the morphology of the fracture. We consider a sharp triangular asperity, invariant in one direction, perturbing an otherwise flat fracture. We investigate its influence on the macroscopic hydraulic transmissivity and heat transfer efficiency, at fixed low Reynolds numb...

Time-dependent advection-diffusion equations arise in mathematical models of porous medium flow and transport processes, including petroleum reservoir simulation, environmental modeling, and other applications. In such applications as immiscible displacement of oil by water in a secondary oil recovery process in petroleum industry or a groundwater transport process involving a non-aqueous phase...

This paper presents a complete dynamic modeling of a membrane distillation process. The model contains two consistent dynamic models. A 2D advection-diffusion equation for modeling the whole process and a modified heat equation for modeling the membrane itself. The complete model describes the temperature diffusion phenomenon across the feed, membrane, permeate containers and boundary layers of...