The improved performance of plasma assisted combustion (PAC) simulations using the fully analytical Jacobian

Abstract

The open-source package ZDPlasKin is integrated into OpenFOAM to develop the ZDP-OF platform, facilitating simultaneous computations of plasma discharge and chemical reactions for plasma assisted combustion (PAC) simulations. To address the computational challenges arising from the disparity between plasma and chemical kinetics, a chemical model program providing a novel fully analytic molar concentration-based Jacobian, CKJac, is introduced, which incorporates computation cost minimization (CCM) strategies and a revised third-body reactions treatment to enhance the efficiency of solving Ordinary Differential Equations (ODE). Then, the efficiency, accuracy, and applicability of CKJac in handling stiff reactions are evaluated by comparing it with other chemistry models, such as pyJac and Standard (a native chemical model in OpenFOAM). The KLU sparse linear algebra library and LAPACK dense linear algebra library are integrated into CVODE and seulex. The effectiveness and robustness of CKJac with stiff ODE solvers, CVODE, and seulex are rigorously validated and demonstrated on four academic configurations: the zero-dimensional (0D) autoignition and PAC under adiabatic homogeneous constant-pressure systems, a two-dimensional (2D) turbulent reacting shear layer case, the three-dimensional (3D) Sandia Flame D, and 2D plasma assisted flame propagation configuration. It is found that CVODE exhibits a requirement for tighter tolerances to achieve high accuracy, and when using the internally generated numerical Jacobian, CVODE demonstrates high robustness. Seulex consistently presents high efficiency and comparable accuracy to CVODE. The low efficiency of CVODE is ascribed to the inefficient linear algebraic equation solving brought by the inherent reinitialization problem in CVODE. CKJac+seulex showcases a notable up to twofold speedup, delivering high accuracy under loose tolerances compared to Standard+seulex. Moreover, CKJac exhibits superior performance compared to pyJac in diverse combustion scenarios due to its low time costs associated with omega and Jacobian formulation evaluations. When combing with linear algebra libraries, pyJac+seulex_LAPACK shows high robustness and CKJac+seulex_KLU shows orders of magnitude speedup for large mechanisms tested in this work.