High-dimensional, unsupervised cell clustering for computationally efficient engine simulations with detailed combustion chemistry

Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering

“…For this reason, a high-dimensional clustering (HDC) algorithm has been implemented [18] and tested. The algorithm was devel oped to deal with multiple and multicomponent fuels in a compu tationally feasible way, by covering the following needs of the detailed chemistry cell clustering problem:…”

“…The final dataset partition may have cluster cen ters containing many member cells as well as completely empty cluster centers. To overcome this problem, a modified version of the fc-means algorithm, named "bounding-box-constrained" kmeans, has been developed and implemented [18]. In traditional f'-means clustering, the final partition is built iteratively: At every iteration, every point is assigned to its closest cluster center, and cluster center positions are then updated based on their net bal ance of lost/gained points.…”

“…Then, the bounding-box approach constrains the cluster centers to remain close to their initialization positions, as each of them, i.e., every vertex in the gridlike representation, can only have member points from its surrounding "boxes," guar anteeing that cluster centers remain well-distributed across the dataset after running the clustering algorithm, still covering the data sparsity in the high-dimensional domain, and ultimately keeping track of the different reactivity conditions of every point. These choices make the computational overhead of the algorithm almost independent on the grid size [18] and negligible in compar ison to the cost of chemistry integration even when the sparse solver is used. A previous study of the effects of species subset S selection, temperature, species mass fraction resolutions sT and eY, and maximum number of grid points along every species dimen sions has shown that fuel species and few other combustion tracer species are enough to capture both local and in-cylinder average properties and that the temperature resolution value gr is the param eter the overall error of the engine simulation with cell clustering is most sensitive to [18], For this reason, the current study was carried out using a high temperature resolution of sr = 10 K. A summary of all the algorithm settings is also reported in Table 1.…”

“…These choices make the computational overhead of the algorithm almost independent on the grid size [18] and negligible in compar ison to the cost of chemistry integration even when the sparse solver is used. A previous study of the effects of species subset S selection, temperature, species mass fraction resolutions sT and eY, and maximum number of grid points along every species dimen sions has shown that fuel species and few other combustion tracer species are enough to capture both local and in-cylinder average properties and that the temperature resolution value gr is the param eter the overall error of the engine simulation with cell clustering is most sensitive to [18], For this reason, the current study was carried out using a high temperature resolution of sr = 10 K. A summary of all the algorithm settings is also reported in Table 1. Once that chemistry has been solved in every cluster center, remapping of the species mass fractions rates of change is done according to the pro cedure developed by Liang et al [31], which verifies both species non-negativity and mass conservation constraints.…”

“…Second, the number of calculations required at every fluid time step is reduced by clustering chemically active cells in the domain into a reduced number of homogeneous clusters, based on an instantaneous high-dimensional representation of the chemical state space that features temperature and a subset of species as its domain [18].…”