Resolvent conditions for discretizations of diffusion-convection-reaction equations in several space dimensions

1998 ◽  
Vol 28 (1) ◽  
pp. 45-67 ◽  
Author(s):  
F.A.J. Straetemans
Keyword(s):  
Diffusion Convection ◽  
Reaction Equations

On the Diffusion-Convection-Reaction Equations

1999 ◽  
Vol 60 (3) ◽  
pp. 207-210 ◽  
Author(s):  
S A El-Wakil ◽  
A Elhanbaly ◽  
M A Abdou
Keyword(s):  
Diffusion Convection ◽  
Reaction Equations

scholarly journals Numerical algorithms for solving the optimal control problem of simple bioreactors

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Raimondas Čiegis ◽  
Remigijus Čiegis
Keyword(s):  
Nonlinear Diffusion ◽  
Finite Difference Methods ◽  
Numerical Algorithms ◽  
External Boundary ◽  
Enzymatic Conversion ◽  
Control Loop ◽  
Potential Accuracy ◽  
Difference Methods ◽  
Diffusion Convection ◽  
Reaction Equations

The modified nonlocal feedback controller is used to control the production of drugs in a simple bioreactor. This bioreactor is based on the enzymatic conversion of substrate into the required product. The dynamics of this device is described by a system of two nonstationary nonlinear diffusion–convection–reaction equations. The analysis of the influence of the convection transport is one the aims of this paper. The control loop is defined using the relation, which shows how the amount of the drug produced in the bioreactor and delivered into a human body depends on the substrate concentration specified on the external boundary of the bioreactor. The system of PDEs is solved by using the finite volume and finite difference methods, the control loop parameters are defined from the analysis of stationary linearized equations. The second aim of this paper is to solve the inverse problem and to determine optimal boundary conditions. These results enable us to estimate the potential accuracy of the proposed devices.  

scholarly journals Impact of Dual Substrate Limitation on Biodenitrification Modeling in Porous Media

Processes ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 890
Author(s):  
Mostafa Abaali ◽  
Jérôme Harmand ◽  
Zoubida Mghazli
Keyword(s):  
A Priori ◽  
Growth Function ◽  
Single Type ◽  
A Priori Error Estimate ◽  
Single Substrate ◽  
Spatially Distributed ◽  
Dual Substrate Limitation ◽  
Diffusion Convection ◽  
Reaction Equations ◽  
Dual Substrate

In this work, we consider a model of the biodenitrification process taking place in a spatially-distributed bioreactor, and we take into account the limitation of the kinetics by both the carbon source and the oxidized nitrogen. This model concerns a single type of bacteria growing on nitrate, which splits into adherent bacteria or free bacteria in the liquid, taking all interactions into account. The system obtained consists of four diffusion-convection-reaction equations for which we show the existence and uniqueness of a global solution. The system is approximated by a standard finite element method that satisfies an optimal a priori error estimate. We compare the results obtained for three forms of the growth function: single substrate limiting, “multiplicative” form, and “minimum” form. We highlight the limitation of the ‘ single substrate limiting model”, where the dependency of the bacterial growth on the nitrate is neglected, and find that the “minimum” model gives numerical results closer to the experimental results.

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