A conservative, positivity preserving scheme for reactive solute transport problems in moving domains

Modeling and analysis of reactive solute transport in deformable channels with wall adsorption–desorption

“…One of the interesting questions to answer is whether ultrasound-induced motion of the arterial walls enhances solvent absorption to the arterial wall. In our recent paper [15], our numerical simulations showed exactly that. In the current manuscript, we focus on the well posedness of that problem.…”

“…It was shown numerically that the solute concentrations remain positive for all times in the blood flow regime. Furthermore, the results of [15] show enhanced drug adsorption by the moving walls as opposed to the rigid walls. This is an important finding that suggests that inducing tissue wall motion using, for example, ultrasound, may enhance cancer drug delivery to the diseased tissue.…”

“…†.t//. In [15], numerical simulations based on this model were applied to the problem of drug transport in elastic arteries. It was shown numerically that the solute concentrations remain positive for all times in the blood flow regime.…”

A nonlinear ALE‐FCT scheme for non‐equilibrium reactive solute transport in moving domains

“…This is coupled with a flux equation on Σ( t ), which describes the transfer of the solutes from the bulk fluid to the wall. This model is proposed in and is an extension of the models studied in to moving domains.…”

On numerical simulation of flow problems in three dimension: energy conservation in fluid-structure interactions

“…Recently, also the numerical simulations are being used for solution of large number of technical or scientific problems and, due to the increase of the computer power, the simulations of complex mathematical models are possible, cf. [1], [2], [3], [4]. Particularly, the turbulent flow under different flow conditions is modelled and numerically approximated in various applications, see e.g.…”