A nonuniform mesh semi-implicit CE–SE method modelling unsteady flow in tapered ducts

Recently, a semi-implicit one-dimensional CE–SE (conservation element–solution element) method for the calculation of the unsteady flow of one and several chemical species tracking in engine ducts has been developed in Arnau et al. [J.M. Arnau, S. Jerez, L. Jódar, J.V. Romero, A semi-implicit conservation element–solution element method for chemical species transport simulation to tapered ducts of internal combustion engine, Math. Comput. Simul. 73 (1/4) (2006) 28–37]. This new scheme improves the accuracy of the original CE–SE with a similar computational cost. In this paper, we modify the semi-implicit CE–SE method taking a nonuniform discretization of the space–time domain. The mesh is constructed by considering the geometrical characteristics of the tapered ducts, which are composed of constant and conical sections. The goal is to reduce the computational cost and to increase the accuracy of the approximated solution. Numerical results of the semi-implicit CE–SE for uniform and nonuniform meshes are compared with experimental data.