Hybrid central–WENO scheme for the large eddy simulation of turbulent flows with shocks

References

• L. Paniagua, O. Lehmkuhl, C. Oliet, and C. D. Pérez-Segarra, Large Eddy Simulations (LES) on the Flow and Heat Transfer in a Wall-Bounded Pin Matrix, Numer. Heat Transfer B, vol. 65, pp. 103–128, 2014.
   Web of Science ®Google Scholar
• S. A. Tkachenko, G. E. Lau, V. Timchenko, G. H. Yeoh, and J. Reizes, Effect of Heat Loss on Turbulent Buoyancy-Driven Flow in a Rectangular Cavity Using the Large-Eddy Simulation, Numer. Heat Transfer A, vol. 70, pp. 689–706, 2016.
   Web of Science ®Google Scholar
• U. Allauddin, M. Klein, M. Pfitzner, and N. Chakraborty, A Priori and a Posteriori Analyses of Algebraic Flame Surface Density Modeling in the Context of Large Eddy Simulation of Turbulent Premixed Combustion, Numer Heat Transfer A, vol. 71, pp. 153–171, 2017.
   Web of Science ®Google Scholar
• N. Gourdain, F. Sicot, F. Duchaine, and L. Gicquel, Large Eddy Simulation of Flows in Industrial Compressors: a Path from 2015 to 2035, Philos. Trans. R. Soc. A, vol. 372, pp. 1–18, 2014.
   Google Scholar
• J. Slotnick, A. Khodadoust, J. Alonso, D. Darmofal, W. Gropp, E. Lurie, and D. Mavriplis, CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences, NASA Langley Research Center, Hampton, VA, USA, 2014 (NASA/CR-2014–218178).
   Google Scholar
• G. S. Jiang and C. W. Shu, Efficient Implementation of Weighted ENO Schemes, J. Comput. Phys., vol. 126, pp. 202–228, 1996.
   Web of Science ®Google Scholar
• B. Thornber, A. Mosedale, and D. Drikakis. On the Implicit Large Eddy Simulations of Homogeneous Decaying Turbulence, J. Comput. Phys., vol. 226, pp. 1902–1929, 2007.
   Web of Science ®Google Scholar
• M. P. Martín, E. M. Taylor, M. Wu, and V. G. Weirs, A Bandwidth-Optimized WENO Scheme for the Effective Direct Numerical Simulation of Compressible Turbulence, J. Comput. Phys., vol. 220, pp. 270–289, 2006.
   Web of Science ®Google Scholar
• N. K. Yamaleev and M. H. Carpenter, A Systematic Methodology for Constructing High-Order Energy Stable WENO Schemes, J. Comput. Phys., vol. 228, pp. 4248–4272, 2009.
   Web of Science ®Google Scholar
• X. Y. Hu, Q. Wang, and N. A. Adams, An Adaptive Central-Upwind Weighted Essentially Non-Oscillatory Scheme, J. Comput. Phys., vol. 229, pp. 8952–8965, 2010.
   Web of Science ®Google Scholar
• Q. Li, Q. Guo, D. Sun, P. Liu, and H. Zhang, A Fourth-Order Symmetric WENO Scheme with Improved Performance by New Linear and Nonlinear Optimizations, J. Sci. Comput., vol. 71, pp. 109–143, 2017.
   Web of Science ®Google Scholar
• N. A. Adams and K. Shariff, A High-Resolution Hybrid Compact-ENO Scheme for Shock-Turbulence Interaction Problems, J. Comput. Phys., vol. 127, pp. 27–51, 1996.
   Web of Science ®Google Scholar
• S. Pirozzoli, Conservative Hybrid Compact-WENO Schemes for Shock-Turbulence Interaction, J. Comput. Phys., vol. 178, pp. 81–117, 2002.
   Web of Science ®Google Scholar
• Y. X. Ren and H. Zhang, A Characteristic-Wise Hybrid Compact-WENO Scheme for Solving Hyperbolic Conservation Laws, J. Comput. Phys., vol. 192, pp. 365–386, 2003.
   Web of Science ®Google Scholar
• N. Mahmoudnejad and K. A. Hoffmann, A Hybrid Scheme for the Numerical Simulation of Shock/Discontinuity Problems, Int. J. Comput. Fluid Dyn., vol. 25, pp. 469–486, 2011.
   Web of Science ®Google Scholar
• G. Stipcich, H. Fu, and C. Liu, High-Order Mixed Weighted Compact and Non-Compact Scheme for Shock and Small Length Scale Interaction, Int. J. Comput. Math., vol. 90, pp. 376–407, 2013.
   Web of Science ®Google Scholar
• D. Kim and J. H. Kwon, A High-Order Accurate Hybrid Scheme Using a Central Flux Scheme and a WENO Scheme for Compressible Flowfield Analysis, J. Comput. Phys., vol. 210, pp. 554–583, 2005.
   Web of Science ®Google Scholar
• D. J. Hill and D. I. Pullin, Hybrid Tuned Center-Difference-WENO Method for Large Eddy Simulations in the Presence of Strong Shocks, J. Comput. Phys., vol. 194, pp. 435–450, 2004.
   Web of Science ®Google Scholar
• X. Wu, and Y. Zhao, A High-Resolution Hybrid Scheme for Hyperbolic Conservation Laws, Int. J. Numer. Methods Fluids, vol.78, pp. 162–187, 2015.
   Web of Science ®Google Scholar
• A. Harten, The Artificial Compression Method for Computation of Shocks and Contact Discontinuities. III. Self-Adjusting Hybrid Schemes, Math. Comput., vol. 32, pp. 363–389, 1978.
   Web of Science ®Google Scholar
• C. Liu, H. Fu, and P. Lu, New Shock Detector and Improved Control Function for Shock-Boundary Layer Interaction, Int. J. Numer. Anal. Model., vol. 9, pp. 276–288, 2012.
   Web of Science ®Google Scholar
• X. Y. Hu, B. Wang, and N. A. Adams, An Efficient Low-Dissipation Hybrid Weighted Essentially Non-Oscillatory Scheme, J. Comput. Phys., vol. 301, pp. 415–424, 2015.
   Web of Science ®Google Scholar
• A. Jameson, W. Schmidt, and E. Turkel, Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge–Kutta Time Stepping Scheme, AIAA Paper-1981–1259, 1981.
   Google Scholar
• F. Ducros, V. Ferrand, F. Nicoud, C. Weber, D. Darracq, C. Gacherieu, and T. Poinso, Large-eddy Simulation of the Shock/Turbulence Interaction, J. Comput. Phys., vol. 152, pp. 517–549, 1999.
   Web of Science ®Google Scholar
• F. Nicoud, F. Ducros, Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor, Flow Turb. Combust., vol. 62, pp. 183–200, 1999.
   Web of Science ®Google Scholar
• M. S. Liou, A Sequel to AUSM, Part II: AUSM+-up for All Speeds, J. Comput. Phys., vol. 214, pp. 137–170, 2006.
   Web of Science ®Google Scholar
• C. Bogey and C. Bailly, Three-Dimensional Non-Reflective Boundary Conditions for Acoustic Simulations: Far Field Formulation and Validation Test Cases, Acta Acust., vol. 88, pp. 463–471, 2002.
   Web of Science ®Google Scholar
• R. Samtaney, D. I. Pullin, and B. Kosovic, Direct Numerical Simulation of Decaying Compressible Turbulence and Shocklet Statistics, Phys. Fluids, vol. 13, pp. 1415–1430, 2001.
   Web of Science ®Google Scholar
• L. Zhao and C. Zhang, A Parallel Unstructured Finite-Volume Method for All-Speed Flows, Numer. Heat Transfer B, vol. 65, pp. 336–358, 2014.
   Web of Science ®Google Scholar
• H. Zhang, Non-Oscillatory and Non-Free-Parameter Dissipation Difference Scheme, Acta Aerodyn. Sin., vol. 6, pp. 143–165, 1988.
   Google Scholar
• N. D. Sandham, Y. F. Yao, and A. A. Lawal, Large-Eddy Simulation of Transonic Turbulent Flow over a Bump, Int. J. Heat Fluid Flow, vol. 24, pp. 584–595, 2003.
   Web of Science ®Google Scholar