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

One-dimensional gas dynamic models are important tools in the design and development of internal combustion engines in the validation stage of a new prototype. These models are defined by nonlinear systems of partial differential equations. Numerous tests are realized in the validation, therefore it is necessary to use efficient numerical methods for solving the nonlinear system. The CE-SE numerical method has a low computational cost. This algorithm is precise in engine ducts with constant area, but its accuracy is reduced in presence of non-smooth changes of the duct area. Recently, we have developed a semi-implicit one-dimensional CE-SE method to the calculation of the unsteady flow of one and several chemical specie tracking in engine ducts. This new numerical scheme improves the precision of the original CE-SE method with a similar computational cost. In this paper, we modify our semi-implicit CE-SE method in order to introduce 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 precision of the approximated solution. Numerical results of the semi-implicit CE-SE for uniform and nonuniform meshes are compared with experimental data.