TY - GEN

T1 - An efficient semi-implicit time-integration scheme for stiff chemical source terms

AU - Xuan, Y.

AU - Savard, B.

AU - Bobbitt, B.

AU - Blanquart, G.

PY - 2014

Y1 - 2014

N2 - In this paper, a semi-implicit iterative time-integration scheme for stiff chemical source terms is proposed, specifically designed for the numerical simulations of unsteady reacting flows with finite-rate chemistry using detailed chemical kinetic mechanisms. This scheme eliminates the expense of inverting the full chemical source Jacobian matrix at each location and time step of a numerical simulation. This is achieved by approximating the chemical source Jacobian matrix by a diagonal matrix, based on the intrinsic relations between the chemical source terms and the species mass fractions. Second order temporal accuracy of this scheme is achieved by using an iterative procedure within each time step. This scheme also possesses better stability characteristics than its explicit counterpart. Furthermore, the convection, diffusion, and chemistry are all integrated simultaneously, which makes this scheme free of lagging errors. The performance of the proposed time-integration scheme is assessed first on a one-dimensional laminar premixed flame. Numerical results show that the new semi-implicit iterative scheme allows for a stable time step size more than 500 times larger than that for the explicit scheme, with almost the same computational cost within each time step. This scheme is also shown to be more efficient computationally than the DASSL solver. This scheme is further applied to the direct numerical simulation of a three-dimensional turbulent premixed flame of n-heptane at a high Karlovitz number.

AB - In this paper, a semi-implicit iterative time-integration scheme for stiff chemical source terms is proposed, specifically designed for the numerical simulations of unsteady reacting flows with finite-rate chemistry using detailed chemical kinetic mechanisms. This scheme eliminates the expense of inverting the full chemical source Jacobian matrix at each location and time step of a numerical simulation. This is achieved by approximating the chemical source Jacobian matrix by a diagonal matrix, based on the intrinsic relations between the chemical source terms and the species mass fractions. Second order temporal accuracy of this scheme is achieved by using an iterative procedure within each time step. This scheme also possesses better stability characteristics than its explicit counterpart. Furthermore, the convection, diffusion, and chemistry are all integrated simultaneously, which makes this scheme free of lagging errors. The performance of the proposed time-integration scheme is assessed first on a one-dimensional laminar premixed flame. Numerical results show that the new semi-implicit iterative scheme allows for a stable time step size more than 500 times larger than that for the explicit scheme, with almost the same computational cost within each time step. This scheme is also shown to be more efficient computationally than the DASSL solver. This scheme is further applied to the direct numerical simulation of a three-dimensional turbulent premixed flame of n-heptane at a high Karlovitz number.

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M3 - Conference contribution

AN - SCOPUS:84943643176

T3 - Western States Section of the Combustion Institute Spring Technical Meeting 2014

SP - 38

EP - 57

BT - Western States Section of the Combustion Institute Spring Technical Meeting 2014

PB - Western States Section/Combustion Institute

T2 - Western States Section of the Combustion Institute Spring Technical Meeting 2014

Y2 - 24 March 2014 through 25 March 2014

ER -