Implementation of the Semi Empirical Kinetic Soot Model within Chemistry Tabulation Framework for Efficient Emissions Predictions in Diesel Engines

Soot prediction for diesel engines is a very important aspect of internal combustion engine emissions research, especially nowadays with very strict emission norms. Computational Fluid Dynamics (CFD) is often used in this research and optimisation of CFD models in terms of a trade-off between accuracy and computational efficiency is essential. This is especially true in the industrial environment where good predictivity is necessary for engine optimisation, but computational power is limited. To investigate soot emissions for Diesel engines, in this work CFD is coupled with chemistry tabulation framework and semi-empirical soot model. The Flamelet Generated Manifold (FGM) combustion model precomputes chemistry using detailed calculations of the 0D homogeneous reactor and then stores the species mass fractions in the table, based on six look-up variables: pressure, temperature, mixture fraction, mixture fraction variance, progress variable and progress variable variance. Data is then retrieved during online CFD simulation, enabling fast execution times while keeping the accuracy of the direct chemistry calculation. In this work, the theory behind the model is discussed as well as implementation in commercial CFD code. Also, soot modelling in the framework of tabulated chemistry is investigated: mathematical model and implementation of the kinetic soot model on the tabulation side is described, and 0D simulation results are used for verification. Then, the model is validated using real-life engine geometry under different operating conditions, where better agreement with experimental measurements is achieved, compared to the standard implementation of the kinetic soot model on the CFD side

A Framework for Algorithm Stability

We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays an important role in a wide variety of areas, such as numerical analysis, machine learning, and topology, but is poorly understood in the context of (combinatorial) algorithms. In this paper we present a framework for analyzing the stability of algorithms. We focus in particular on the tradeoff between the stability of an algorithm and the quality of the solution it computes. Our framework allows for three types of stability analysis with increasing degrees of complexity: event stability, topological stability, and Lipschitz stability. We demonstrate the use of our stability framework by applying it to kinetic Euclidean minimum spanning trees

Topological Stability of Kinetic kk-Centers

We study the $k$-center problem in a kinetic setting: given a set of continuously moving points $P$ in the plane, determine a set of $k$ (moving) disks that cover $P$ at every time step, such that the disks are as small as possible at any point in time. Whereas the optimal solution over time may exhibit discontinuous changes, many practical applications require the solution to be stable: the disks must move smoothly over time. Existing results on this problem require the disks to move with a bounded speed, but this model is very hard to work with. Hence, the results are limited and offer little theoretical insight. Instead, we study the topological stability of $k$-centers. Topological stability was recently introduced and simply requires the solution to change continuously, but may do so arbitrarily fast. We prove upper and lower bounds on the ratio between the radii of an optimal but unstable solution and the radii of a topologically stable solution---the topological stability ratio---considering various metrics and various optimization criteria. For $k = 2$ we provide tight bounds, and for small $k > 2$ we can obtain nontrivial lower and upper bounds. Finally, we provide an algorithm to compute the topological stability ratio in polynomial time for constant $k$