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Show ") Appendix Inviscid Flux Jacobians The generic expression for the convective part of the inviscid flux Jacobians, ? K , $£- and ^fr is written for a generalized iV-species reacting system as r/wj 0 0 ^ RT ^y Uw L t/^r, + K; RT UW2 RT 0 C/ U DT I rV£ C/w^ 4- «; unt2R-f 0 0 RT \J IX p T i ^J RT1 1/ £/w^f +KZ Pl*x P2*x pNKx p(U +UKX) pVKx PWKX P\Ky P2*y PlSJrty PUKy P(U + VKy) PWKy Pl*z P2*z pNK: PUKZ pVKz p(U + WKZ UhtN^£ P(UU + H K X ) p(vU + Hriy) p(wU + Hhi where U = Kxu-\-Kyv+Kzw is the contravariant velocity; the generic metric terms, K, = £ for H c = Ec, K = n for H c = Fc and n = C for H r = G c Viscous Flux Jacobians The generic expression for the viscous flux Jacobians, HKK is written for a generalized iV-species reacting system as KKK~ J AAJi(l-Ii) \Dinp\Yx ADlmfaY2 ADlmp2(l-Y2) AD^^YN) 0 0 0 Aft(/ii -hm) ADlm(32YN 0 0 0 A(32(h2-hm) A-D^jtWi ADimt3NY2 ADimPN(l-YN) 0 0 0 A/3N(hN - hm) Pe^- 7T„ 0 K,K, o /ie(A+ -f) 3 pe^ Pe(A+^-) pe\ Pe(A+ ^ /Ze 3 7Tlr 7T», where the generic metric terms, K = £ for R K K = R ^, «: = n for R K K = R^^ and K = £ for RK/C = R<^; and 0 0 0 0 0 0 KAC Pm J .2 , .„2 A = Kx + rZy 4" K. A = /?i?T T|| = /ie[(A 4- - ^ ) _ 4- - y ^ + " ^p • < / ' 7Tt, = /if ivyK>X K? u 4 (A 4- -^f)-4- /Cy /"C; -7/M -y-_ 4- -r-^U 4- (A 4- y)-j 11 |