Abstract
The present 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 the 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 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.
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