Pseudotransient continuation for combustion simulation with detailed reaction mechanisms. (English) Zbl 1382.65195
Summary: We study pseudotransient continuation \((\Psi\mathrm{tc})\) as a nonlinear solver for implicit discretizations of combustion problems with detailed chemical models. Detailed models produce extreme stiffness, nonlinearity, and a transient instability associated with ignition/extinction phenomena. These are challenges to traditional Newton methods that are well met by \(\Psi\mathrm{tc}\). We develop and study several adaptive \(\Psi\mathrm{tc}\) methods on autoignition problems, including detailed chemical mechanisms from hydrogen to n-heptane. Using a periodic reactor with repeated ignition/extinction events, we demonstrate the efficiency that \(\Psi\mathrm{tc}\) offers relative to traditional solution techniques. We compare the efficiency of physical time discretizations of the backward difference formula and implicit Runge-Kutta types, as well as their numerical convergence behavior on slowly evolving solutions.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 80M25 | Other numerical methods (thermodynamics) (MSC2010) |
| 80A25 | Combustion |
Keywords:
detailed combustion chemistry; time integration; pseudotransient continuation; dual time-stepping; backward differentiation formulas; diagonally implicit Runge-Kutta methodsReferences:
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