As more emphasis is placed worldwide on reducing greenhouse gas emissions, automobile manufacturers have to create more efficient engines. Simultaneously, legislative agencies want these engines to produce fewer problematic emissions such as nitrogen oxides and particulate matter. In response, new technology, like homogeneous charge compression ignition and fuel cells, are being researched alongside lean-burning engines like the compression ignition or diesel engine. These newer engines present a number of benefits but still have significant challenges to overcome. As a result, renewed interest has risen in making lean-burning engines cleaner. The key to cleaning up the lean-burning engine is the placement of aftertreatment devices in the exhaust. These devices have shown great potential in reducing emission levels below regulatory levels while still allowing for increased fuel economy versus a traditional gasoline engine. However, these devices are subject to many flow control issues. While experimental evaluation of these devices helps to understand these issues better, it is impossible to solve the problem through experimentation alone because of time and cost constraints. Because of this, accurate models are needed in conjunction with the experimental work. In this dissertation, the author examines the entire exhaust system including reacting gas dynamics and aftertreatment devices, and develops a complete numerical model for it. The author begins by analyzing the current one-dimensional gas-dynamics simulation models used for internal combustion engine simulations. It appears that a more accurate and faster numerical method is available, in particular, those developed in aeronautical engineering, and the author successfully implements one for the exhaust system. The author then performs a comprehensive literature search to better understand the different aftertreatment devices. A number of these devices require a secondary injection of fuel or reductant in the exhaust stream. Accordingly, the author develops a simple post-cylinder injection model which can be easily calibrated to match experimental findings. In addition, the author creates a general catalyst model which can be used to model virtually all of the different aftertreatment devices. Extensive validation of this model with experimental data is presented along with all of the numerical algorithms needed to reproduce the model.

Local preconditioning for the Navier-Stokes equations may be called optimal if it equalizes all propagation and dissipation time-scales, for all combinations of Mach number and Reynolds number. Previously designed preconditioners are ineffective for certain combinations of low Reynolds number and low Mach number; in addition some of these create a growing mode, making the PDE-system unstable. (Users may regain stability through an implicit discretization.) In this paper we first review the forms and properties of all previously published N-S preconditioners on the basis of the 1-D N-S equations, then derive an optimal preconditioning matrix for these equations. We find again that it creates an unstable mode; a sensitivity analysis shows that optimal preconditioning and stability are mutually exclusive. Two possible remedies are suggested and briefly investigated: (1) to redefine the complex condition number in a way more appropriate for explicit discretizations; (2) to reformulate the N-S equations as a larger first-order system of hyperbolic-relaxation equations and base the preconditioner on this system. The latter approach appears most promising.