Application of approximate chemical Jacobians for constant volume reaction and shock-induced combustion Original Research Article

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.