Variable Time-stepping Exponential Integrators for Chemical Reactors with Analytical Jacobians

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Chemical combustion problems are known to be stiff and therefore difficult to efficiently integrate in time when numerically simulated. Implicit methods, such as backwards differentiation formula (BDF), are widely considered to be the state-of-the-art methods owing their capability of taking relatively large time-steps while maintaining accurate combustion characteristics. Exponential time integration methods have recently demonstrated the ability to accurately and efficiently solve large scale systems of ordinary differential equations. This study introduces a novel adaptive time stepping exponential integrator named EPI3V. Its performance is measured on spatially homogeneous isobaric reactive mixtures involving three hydrocarbon fuel mechanisms. The full combustion process is simulated using gas compositions with sufficient temperature to obtain auto-ignition. Simulations are run until the steady state is obtained, then a comparison of the computational efficiency and accuracy between a BDF and EPI3V method is made. The novel EPI3V method exhibits comparable computational efficiency to a well-established implementation of the variable time-stepping BDF implicit methods for two of the mechanisms investigated. In certain situations it even demonstrates a slight advantage over the implicit solver. However, in one specific case, the EPI3V shows relative performance degradation compared to the implicit method, but it still converges for this case. These results indicate that exponential time integration methods may be applicable to a larger variety of combustion problems.