Tang, Qing; Pope, Stephen B. A more accurate projection in the rate-controlled constrained-equilibrium method for dimension reduction of combustion chemistry. (English) Zbl 1068.80539 Combust. Theory Model. 8, No. 2, 255-279 (2004). Summary: The rate-controlled constrained-equilibrium (RCCE) method for dimension reduction of combustion chemistry is revisited from a geometric viewpoint. A constrained equilibrium manifold (CEM) is defined as all compositions that satisfy the maximum-entropy or minimum-free energy conditions of the gas mixture, subject to specified constraints. The RCCE method is based solely on thermodynamics, and it is shown that this method contains a hidden assumption of an orthogonal projection that projects the rate equation of the chemical system onto the CEM. An extension of the RCCE method is constructed by making an alternative projection based on the conjecture that, near the CEM, there is a close parallel inertial manifold (CPIM). The CPIM assumption introduces the chemical kinetics directly through the local Jacobian and hence leads to greater accuracy than RCCE. The comparison between the RCCE method and its extension is made in the test calculations of hydrogen-air and methane-air autoignition. Cited in 7 Documents MSC: 80M25 Other numerical methods (thermodynamics) (MSC2010) 65L99 Numerical methods for ordinary differential equations 80A25 Combustion Software:STANJAN PDFBibTeX XMLCite \textit{Q. Tang} and \textit{S. B. Pope}, Combust. Theory Model. 8, No. 2, 255--279 (2004; Zbl 1068.80539) Full Text: DOI References: [1] Bischof C, Sci. Programming 1 pp 1– (1992) [2] DOI: 10.1080/713665325 · Zbl 1045.80500 · doi:10.1080/713665325 [3] DOI: 10.1088/1364-7830/4/1/304 · Zbl 0953.80001 · doi:10.1088/1364-7830/4/1/304 [4] Bodenstein M, Z. Phys. Chem. 57 pp 168– (1906) [5] DOI: 10.1016/0098-1354(85)85014-6 · doi:10.1016/0098-1354(85)85014-6 [6] DOI: 10.1080/00102208908924038 · doi:10.1080/00102208908924038 [7] Gordon G H, Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications pp 1311– (1994) [8] DOI: 10.1080/713665370 · Zbl 0928.92039 · doi:10.1080/713665370 [9] DOI: 10.1016/0360-1285(90)90046-6 · doi:10.1016/0360-1285(90)90046-6 [10] DOI: 10.1016/S0010-2180(71)80166-9 · doi:10.1016/S0010-2180(71)80166-9 [11] Li G Y, J. Phys. Chem. 105 pp 7765– (2001) [12] DOI: 10.1016/0010-2180(92)90034-M · doi:10.1016/0010-2180(92)90034-M [13] Maas U, Proc. Combust. Inst. 22 pp 1695– (1988) [14] DOI: 10.1088/1364-7830/6/4/308 · doi:10.1088/1364-7830/6/4/308 [15] DOI: 10.1016/0010-2180(87)90057-5 · doi:10.1016/0010-2180(87)90057-5 [16] DOI: 10.1080/713665229 · Zbl 1046.80500 · doi:10.1080/713665229 [17] Pope S B, Combust. Flame (2004) [18] Reynolds W C, The Element Potential Method for Chemical Equilibrium Analysis: Implementation in the Interactive Program STANJAN (1986) [19] Smith G P, et al (1999) [20] DOI: 10.1007/BFb0035362 · doi:10.1007/BFb0035362 [21] Sung C J, Proc. Combust. Inst. 27 pp 295– (2001) · doi:10.1016/S0082-0784(98)80416-5 [22] Tang Q, PhD Thesis (2003) [23] DOI: 10.1016/S1540-7489(02)80173-0 · doi:10.1016/S1540-7489(02)80173-0 [24] DOI: 10.1016/S0082-0784(00)80204-0 · doi:10.1016/S0082-0784(00)80204-0 [25] Tomlin A S, Comprehensive Chemical Kinetics 35: Low-Temperature Combustion and Autoignition (1997) [26] Tonse S R, Israel J. Chem. 39 pp 97– (1999) · doi:10.1002/ijch.199900010 [27] DOI: 10.1016/0097-8485(94)80022-7 · doi:10.1016/0097-8485(94)80022-7 [28] DOI: 10.1016/S0010-2180(97)00334-9 · doi:10.1016/S0010-2180(97)00334-9 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.