2005
DOI: 10.1007/s00021-005-0151-0
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The Role of Abstract Numerical Properties in the Change of Character of Reactive Flows

Abstract: 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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Cited by 1 publication
(3 citation statements)
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“…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%
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“…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%
“…Methods EIE and EEE are globally first order methods. The qualitative behaviour of EEE and EIE is studied in [17].…”
Section: Qualitative Behaviourmentioning
confidence: 99%
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