UC Merced

Computational combustion plays a major role in engineering applications. However, solving the large systems of differential equations that model combustive processes is challenging. One of the major computational difficulties with the numerical modeling of combustion lies in the widely varying time scales present in the model equations that describe chemical interactions of species with the fluid and thermodynamic transport phenomena. The resulting dramatic stiffness ofthe equations demands the development of more efficient temporal integrators to enable efficient and accurate combustion simulation.

Traditionally, the stiffness of computational combustion models has been addressed using implicit methods. However, the performance of the implicit schemes depends highly on the availability of an efficient preconditioner to alleviate stiffness constraints. Additionally, due to the complexity of the coupling between chemistry, fluid, and transport phenomena, splitting is often used to simplify the time integration of the model equations. Splitting, in turn, reduces the accuracy of theapproximation. While constructing a preconditioner for a portion of the source terms, such as chemical reactions, is feasible, this task becomes more complicated if one considers the full source term of the equations.

Exponential integrators have recently emerged as an efficient alternative to implicit methods for solving large-scale stiff systems, particularly when no effective preconditioner is available. In this thesis, we explore whether exponential methods can be used for combustion simulations and study the computational advantages of such schemes.

We first explore how to tackle the stiff nature of chemical kinetics in a model that forgoes transport phenomena to isolate the chemical kinetics terms and forms the core of various more complex combustion models. A novel time adaptive exponential integrator is presented and then applied to this zero-dimensional (Zero-D) combustion problem. We demonstrate that the new method can perform comparably to well-established implicit-Krylov time integration methods. We study the performance of the exponential integration methods and demonstrate how theyare affected by the spectrum of the problem.

We then extend the chemical kinetics core to include transport phenomena and develop an exponential integration-based numerical approach to the propagating flame front model in one dimension. In addition to the embedded homogeneousreactor problem, advection and diffusion terms are added, and continuity is considered, which generates a highly coupled system of PDEs. In these problems, operator splitting is typically used to separate the stiff chemical reaction source terms from the much slower transport phenomena. Effectively, this reduces the equations to a Zero-D problem and a transport problem, which needs to be solved at each time step. While effective, this introduces unfavorable splitting errors; we demonstrate that this split can be avoided when using an exponential time integration scheme. We study the performance of the new exponential integration approach for the model using several different chemical mechanisms and compare the performance of the new integrators to the state-of-the-art NGA code, which uses implicit methods.

Our computational models and numerical experiments indicate that exponential methods offer a promising approach to modeling combustion and highlight directions for further studies that can help to develop more efficient time integra-tors for computational combustion problems.