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Application of approximate chemical Jacobians for constant volume reaction and shock-induced combustion. (English) Zbl 1044.76039

Summary: The study suggests an approximate Jacobian, the Gauss-Seidel partial Jacobian, derived from the concept of preconditioned time differencing methods, and includes it into the LU-SGS (lower upper symmetric Gauss-Seidel) scheme. The validity of the Gauss-Seidel partial Jacobian is demonstrated by calculating a constant volume reaction, and by comparing the results with those of other approximate Jacobians. Then, the performance of LU-SGS scheme is examined by stability analyses and computations of shock-induced combustions. The results show that the LU-SGS scheme with the Gauss-Seidel partial Jacobian is as stable and accurate as the full Jacobian, and is about \(5-30\%\) faster than those with the full Jacobian, while the scheme with other approximate Jacobians produces satisfactory results only at small time step sizes.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76V05 Reaction effects in flows
80A25 Combustion
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