1. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 Logical steps for the incorporation of chemical kinetics in internal combustion engine simulations Figure Legend:

2. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 CPU time comparison of the adiabatic constant volume problem ODE functions using the SpeedCHEM package at different reaction mechanism dimensions [4,19–23] Figure Legend:

3. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 Jacobian matrix sparsity pattern for the ERC multiChem [5] mechanism. Both axes represent the species indices in the reaction mechanism. Figure Legend:

4. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 Sample schematic of the gridlike initialization procedure, in two dimensions. Points represent the dataset; diamond marks the initial cluster centers. Figure Legend:

5. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 Reference engine sector mesh adopted for the current study Figure Legend:

6. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 Average in-cylinder pressure and apparent heat release rate comparison for the three cases considered, (solid lines) CHEMKIN versus (dashed lines + marks) SpeedCHEM chemistry solver Figure Legend:

7. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 CPU time comparison between KIVA simulations with detailed chemistry when either using Chemkin-II or SpeedCHEM as the chemistry solver. Values are reported for chemistry/fluid flow only parts. Figure Legend:

8. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 In-cylinder pressure trace predictions with different grid resolutions. Full chemistry solution (solid lines) versus high-dimensional clustering (dashed lines + marks). Figure Legend:

9. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 Pollutant predictions at different grid resolutions: carbon monoxide (top), unburned hydrocarbons (center), nitrogen oxides (bottom). Full chemistry solution (solid lined) versus high-dimensional clustering (dashed lines + marks). Figure Legend:

10. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 Local temperature distribution on a vertical cut-plane, case 1, grid 4, 2.0 deg ATDC, (bottom) full chemistry solution versus (top) high-dimensional clustering Figure Legend:

11. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 Local NO x mass fractions on a vertical cut-plane, case 1, grid 4, 2.0 deg ATDC, (bottom) full chemistry solution versus (top) high- dimensional clustering Figure Legend:

12. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 Local CO mass fractions on a vertical cut-plane at 2.0 deg after TDC, (bottom) full chemistry solution versus (top) high-dimensional clustering Figure Legend:

13. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 In-cylinder pressure trace predictions at case 2 and case 3, grids 3 and 4. Full chemistry solution (solid lines) versus high- dimensional clustering (dashed lines + marks). Figure Legend:

14. Date of download: 7/7/2016 Copyright © ASME. All rights reserved. From: Computationally Efficient Simulation of Multicomponent Fuel Combustion Using a Sparse Analytical Jacobian Chemistry Solver and High-Dimensional Clustering J. Eng. Gas Turbines Power. 2014;136(9):091515-091515-11. doi:10.1115/1.4027280 CPU time performance of the HDC algorithm at different grid resolutions. Full chemistry KIVA simulations (squares) versus clustered KIVA simulations (triangles). Speed-up factors refer to the CPU time spent on chemistry only. Figure Legend: