Combustion Modeling of Dual-fuel Engines

Energy security concerns and abundant supply of Natural Gas in US provide impetus for engine designers to consider alternative gaseous fuels in existing engines. Dual-fuel Natural Gas (NG) engine concept is attractive due to minimal design changes, ability to preserve high Compression ratio (CR) of the baseline diesel, and reduce fuel cost without imposing consumer range anxiety. However, increased complexity of the dual-fuel engine poses challenges, including auto-ignition of end NG-air mixture (knock) at high loads, flame propagation limit at low load and transient response of an engine with directly injected diesel fuel and injection of Compressed NG upstream of the intake manifold. Predictive simulation of the complete engine system is an invaluable tool for investigations of such conditions and development of dual-fuel control strategies. Simulation work gives a better understanding of dual-fuel combustion nature, enables investigation of a broader operating space and complement results by providing values of parameters that cannot be easily measured from experiment. Additionally, with increased complexity of modern engines, map-based control becomes abundant and costly. A combustion model with sufficient level of predictiveness and reasonable requirement on calculation effort enables opportunities for model based control development

A parallel-in-time algorithm for high-order BDF methods for diffusion and subdiffusion equations

In this paper, we propose a parallel-in-time algorithm for approximately solving parabolic equations. In particular, we apply the $k$-step backward differentiation formula, and then develop an iterative solver by using the waveform relaxation technique. Each resulting iteration represents a periodic-like system, which could be further solved in parallel by using the diagonalization technique. The convergence of the waveform relaxation iteration is theoretically examined by using the generating function method. The approach we established in this paper extends the existing argument of single-step methods in Gander and Wu [Numer. Math., 143 (2019), pp. 489--527] to general BDF methods up to order six. The argument could be further applied to the time-fractional subdiffusion equation, whose discretization shares common properties of the standard BDF methods, because of the nonlocality of the fractional differential operator. Illustrative numerical results are presented to complement the theoretical analysis