The use of splitting methods in the numerical simulation of reacting flows

Araújo, Adérito; Ferreira, J. A.; Oliveira, Paula de; Patrício, Miguel; Rosa, Paulo

doi:10.1007/s00791-003-0109-9

Cited by 7 publications

(7 citation statements)

References 6 publications

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“…It is proved in [18] that, if no boundary condition is considered, that is, if z 2 R; then p(t s + 1 ) = y(t s + 1 ) which means that there is no functional splitting error. However, if a boundary condition is included at z = 0, then kp(t s + 1 ) À y(t s + 1 )k 1 = O(Dt).…”

Section: Methodsmentioning

confidence: 99%

“…As problem (16)- (18), for the digester model, exhibits different qualitative behaviour for z 6 z s,EXT and z s,EXT 6 z 6 z b , different families of splitting methods are used in each part of the digester.…”

Section: Numerical Splittingmentioning

confidence: 99%

“…For z 6 z s,EXT the profiles of concentrations and temperature present big gradients due to the sharp changes imposed in the circulations and also to the reaction speeds. To cope with this situation, (16)- (18) is solved with an EIE method obtained by patching together an explicit upwind Smolarkiewicz method -E -to solve (16) and (18) and the implicit Euler method -I -to solve (17). The resulting EIE splitting method is defined by…”

Section: Numerical Splittingmentioning

confidence: 99%

“…In cases where the model exhibits significant stiffness, different choices are more suitable as, for example, second order implicit methods for reaction Eq. (17) and nonlinear flux limiters methods for (16) and (18).…”

Section: Qualitative Behaviourmentioning

confidence: 99%

“…Splitting methods have been studied by several authors [12][13][14][15][16]. A mathematical analysis of convergence for the method used in this paper is developed in [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Using splitting methods in continuous digester modeling

Araújo

Ferreira

Fernandes

et al. 2008

Applied Mathematical Modelling

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The pulp and paper industry plays an important role in European economies. The chemical reactions that transform wood chips in pulp occur mainly in a complex moving bed reactor, the digester. Nowadays the use of mathematical models to simulate the transient behaviour of the digester in terms of temperature and compound concentrations represents a real need for industry because it allows simulation of experiments that can not be afforded or that might be very risky. The digester -the most critical piece of the equipment of a pulp mill -is a heterogeneous reactor with an almost cylindrical shape, where wood chips react with an aqueous solution of sodium hydroxide and sodium sulfide, to remove the lignin from the cellulose fibers. From a mathematical point of view the dynamical behaviour of the reactor can be represented by a system of hyperbolic nonlinear partial differential equations. In this system, with 15 equations, we can identify three main types: the equations that describe the temperature and the concentration respectively of the solid, entrapped liquid and free liquid phase. Each of these type of equations present a certain complexity, its numerical simulation being a hard task. In this sense we point out the high nonlinearity of the functions that represent the chemical reactions; the discontinuities induced by the extraction and injection of the free liquor; the discontinuities in the convection velocity of the free liquor -positive where the liquid flown downwards and negative where the free liquid flows upwards. Numerical methods based on operator splitting, nonuniform refinement and some particular techniques to smooth discontinuities, are studied from a qualitative and quantitative viewpoint. Several simulations on temperature and concentrations of organic and inorganic compounds are presented. Special attention will be devoted to the effects induced in the process by discontinuities of wood chips composition.

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Section: Methodsmentioning

confidence: 99%

Section: Numerical Splittingmentioning

confidence: 99%

Section: Numerical Splittingmentioning

confidence: 99%

Section: Qualitative Behaviourmentioning

confidence: 99%

“…Splitting methods have been studied by several authors [12][13][14][15][16]. A mathematical analysis of convergence for the method used in this paper is developed in [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Using splitting methods in continuous digester modeling

Araújo

Ferreira

Fernandes

et al. 2008

Applied Mathematical Modelling

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The Role of Abstract Numerical Properties in the Change of Character of Reactive Flows

Araújo

Ferreira

Oliveira

2005

J. math. fluid mech.

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Abstract. The aim of this paper is to study the role of explicitness, implicitness and order in the stability and qualitative properties of splitting methods for solving advection-reaction equations. Numerical pathologies produced by simulations are identified which allow the correction of wrong numerical reactive flows. Several numerical examples which show the effectiveness of our approach are presented. Mathematics Subject Classification (2000). 65M06, 65M20, 65M15.

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High resolution numerical simulation of triple point collision and origin of unburned gas pockets in turbulent detonations

Mahmoudi

Mazaheri

2015

Acta Astronautica

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The use of splitting methods in the numerical simulation of reacting flows

Cited by 7 publications

References 6 publications

Using splitting methods in continuous digester modeling

Using splitting methods in continuous digester modeling

The Role of Abstract Numerical Properties in the Change of Character of Reactive Flows

High resolution numerical simulation of triple point collision and origin of unburned gas pockets in turbulent detonations

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