Singular perturbed vector field method applied to combustion in diesel engine: Continuous case with thermal runaway

In this study, we employ the well-known method of a singularly perturbed vector field (SPVF) and its application to the thermal runaway of diesel spray combustion. Given a system of governing equations, consisting of hidden multi-scale variables, the SPVF method transfers and decomposes such a system into fast and slow singularly perturbed subsystems. The resulting subsystem enables us to better understand the complex system and simplify the calculations. Powerful analytical, numerical, and asymptotic methods (e.g., the method of slow invariant manifolds and the homotopy analysis method) can subsequently be applied to each subsystem. In this paper, we compare the results obtained by the methods of slow invariant manifolds and SPVF, as applied to the spray (polydisperse) droplets combustion model.