Convergence Analysis of Mixed Numerical Schemes for Reactive Flow in a Porous Medium

2013 ◽  
Vol 51 (4) ◽  
pp. 2283-2308 ◽  
Author(s):  
K. Kumar ◽  
I. S. Pop ◽  
F. A. Radu
2019 ◽  
Vol 25 ◽  
pp. 65 ◽  
Author(s):  
Dorothee Knees

It is well known that rate-independent systems involving nonconvex energy functionals in general do not allow for time-continuous solutions even if the given data are smooth. In the last years, several solution concepts were proposed that include discontinuities in the notion of solution, among them the class of global energetic solutions and the class of BV-solutions. In general, these solution concepts are not equivalent and numerical schemes are needed that reliably approximate that type of solutions one is interested in. In this paper, we analyse the convergence of solutions of three time-discretisation schemes, namely an approach based on local minimisation, a relaxed version of it and an alternate minimisation scheme. For all three cases, we show that under suitable conditions on the discretisation parameters discrete solutions converge to limit functions that belong to the class of BV-solutions. The proofs rely on a reparametrisation argument. We illustrate the different schemes with a toy example.


2001 ◽  
Vol 12 (5) ◽  
pp. 557-569 ◽  
Author(s):  
J. CHADAM ◽  
P. ORTOLEVA ◽  
Y. QIN ◽  
R. STAMICAR

The shape stability of the reaction interface for reactive flow in a porous medium is investigated. Previous work showed that the Reaction-Infiltration Instability could cause the reaction zone to lose stability when the Peclet number exceeded a critical value. The new feature of this study is to include a velocity-dependent hydrodynamic dispersion. A mathematical model for this phenomenon is given in the form of a moving free-boundary problem. The spectrum of the linearized problem is obtained, and the related analysis and numerical calculations show that the onset of the instability is not eliminated by the new dispersive terms. The details of analysis show that the instability is reduced especially by the transverse dispersion.


1999 ◽  
Vol 67 (4) ◽  
pp. 749-757 ◽  
Author(s):  
G. Rajesh ◽  
R. B. Bhagat ◽  
K. A. Fichthorn

This study develops an integrated micro-macro model of reactive flow in a porous medium consisting of spatially periodic hexagonal array of solid reacting cylinders. The micro model describes the growth of reaction product on the solid reactant surface. The macro flow of the infiltrant fluid is described by Darcy’s law. The transient permeability and thus advancement of the infiltration front are determined as a function of process parameters from the micro model. Crucial process parameters that influence the advance of the fluid front are identified. The results from this investigation can be used to optimize the manufacture of ceramic-matrix composites. [S0021-8936(00)02703-3]


2016 ◽  
Vol 71 (1) ◽  
pp. 329-347 ◽  
Author(s):  
Christine Bernardi ◽  
Jad Dakroub ◽  
Gihane Mansour ◽  
Farah Rafei ◽  
Toni Sayah

2018 ◽  
Vol 19 (2) ◽  
pp. 333-374 ◽  
Author(s):  
Jérôme Droniou ◽  
Robert Eymard ◽  
Alain Prignet ◽  
Kyle S. Talbot

2019 ◽  
Vol 8 (1) ◽  
pp. 69-78 ◽  
Author(s):  
Inayat Ullah ◽  
M.T. Rahim ◽  
Hamid Khan ◽  
Mubashir Qayyum

Author(s):  
I. G. Baoku ◽  
K. I. Falade

This article is concerned with the study of heat and mass transfer of a MHD reactive flow of an upper-convected Maxwell fluid model over a stretching surface subjected to a prescribed heat flux with velocity slip effect in a Darcian porous medium in the presence of thermal radiation and internal heat generation/absorption. The basic boundary layer governing partial differential equations are transformed into a set of coupled ordinary differential equations, which are solved numerically using Runge-Kutta-Fehlberg integration scheme with shooting technique. The far field boundary conditions are asymptotically satisfied to support the accuracy of the numerical computations and the results obtained. The velocity, temperature and species concentration profiles are enhanced by increasing values of velocity slip parameter with Hartmann number, heat generation/absorption parameter and order of chemical reaction parameter respectively.  Increments in the values of velocity slip parameter, Hartmann number, rate of chemical reaction parameter and Prandtl number boost the wall shear stress, dimensionless surface temperature is increased by increasing values of Deborah number, heat generation/absorption and order of chemical reaction parameters while local rate of mass transfer is enhanced by increments in the values of Hartmann number, suction velocity, Darcian porous medium, rate of chemical reaction and velocity slip parameters. The presence of velocity slip on the flow distribution is found to be of great significance to the study.


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