A Sharp-Interface Immersed Boundary Method for High-Speed Compressible Flows

  • Shuvayan Brahmachary
  • Ganesh NatarajanEmail author
  • Vinayak Kulkarni
  • Niranjan Sahoo
Part of the Computational Methods in Engineering & the Sciences book series (CMES)


Numerical simulation of hypersonic flows is important owing to their applications to the design of launch vehicles and re-entry capsules. We describe the development and application of a hybrid Cartesian–immersed boundary (HCIB) approach in a finite volume (FV) framework for inviscid and viscous compressible flows with a focus on the hypersonic regime. The HCIB approach employs a local one-dimensional reconstruction to obtain the near-wall solutions thereby enforcing the boundary conditions exactly on the sharp geometric interface. The role of the reconstruction on solution accuracy and discrete conservation is discussed, and the IB-FV solver is applied to several hypersonic flow problems involving inviscid as well as viscous flows. The studies demonstrate the efficacy of the HCIB approach for inviscid flows with stationary as well as moving bodies while also highlighting some of the drawbacks for heat transfer predictions in high Reynolds number flows. Some directions for future research are also outlined.


Sharp interface Immersed boundary Discrete conservation Heat transfer Hypersonic flows 



The financial support through ISRO-RESPOND project during the course of this work is gratefully acknowledged. The authors would also like to thank Mr. Vinod Kumar and Dr. V. Ashok from VSSC Thiruvananthapuram for their valuable comments on the work.


  1. Arienti M, Hung P, Morano E, Shepherd JE (2003) A level set approach to Eulerian-Lagrangian coupling. J Comput Phys 185:213–251. Scholar
  2. Arslanbekov RR, Kolobov VI, Frolova AA (2011) Analysis of compressible viscous flow solvers with adaptive Cartesian mesh. In: 20th AIAA computational fluid dynamics conference, Honolulu, Huwaii.
  3. Blazek J (2001) Computational fluid dynamics: principles and applications. Elsevier, AmsterdamzbMATHGoogle Scholar
  4. Brahmachary S (2019) Finite volume/immersed boundary solvers for compressible flows: development and applications. Ph.D. thesis dissertation, Indian Institute of Technology GuwahatiGoogle Scholar
  5. Brahmachary S, Natarajan G, Kulkarni V, Sahoo N (2018) A sharp-interface immersed boundary framework for simulations of high-speed inviscid compressible flows. Int J Numer Methods Fluids 86:770–791. Scholar
  6. Brehm C, Hader C, Fasel HF (2015) A locally stabilized immersed boundary method for the compressible Navier-Stokes equations. J Comput Phys 295:475–504. Scholar
  7. Cho Y, Chopra J, Morris PJ (2007) Immersed boundary method for compressible high-Reynolds number viscous flow around moving bodies. AIAA 2007-125:
  8. Clarke DK, Salas MD, Hassan HA (1986) Euler calculations for multi-element airfoils using Cartesian grids. AIAA 24:353–358. Scholar
  9. Das P, Sen O, Jacobs G, UdayKumar HS (2017) A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows. Int J Comput Fluid Dyn 31:269–291. Scholar
  10. de Tullio MD, Palma PD, Iaccarino G, Pascazio G, Napolitano M (2007) An immersed boundary method for compressible flows using local grid refinement. J Comput Phys 225:2098–2117. Scholar
  11. Ghias R, Mittal R, Dong H (2007) A sharp interface immersed boundary method for compressible viscous flows. J Comput Phys 225:528–553.
  12. Ghosh S, Choi JI, Edwards JR (2010) Numerical simulations of effects of micro vortex generators using immersed-boundary methods. AIAA 48:92–103. Scholar
  13. Gilmanov A, Sotiropoulos F (2005) A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies. J Comput Phys 207:457–492. Scholar
  14. Gustaffson B, Enander EP, Sjogreen B (1991) Solving flow equations for high Mach numbers on overlapping grids. In: Hypersonic flows for reentry problems, pp 585–599. Springer, BerlinGoogle Scholar
  15. Holden MS (1978) A study of flow separation in regions of shock wave-boundary layer interaction in hypersonic flow. In: AIAA 11th fluid and plasma dynamics conference, Seattle, Washington.
  16. John B, Kulkarni V (2014) Numerical assessment of correlations for shock wave boundary layer interaction. Comp Fluids 90:42–50. Scholar
  17. Lillard R, Dries K (2005) Laminar heating validation of the overflow code. In: 43rd AIAA aerospace sciences meeting and exhibit, p. 689.
  18. Liuo MS, Steffen CJ Jr (1993) A new flux splitting scheme. J Comput Phys 107:23–39. Scholar
  19. Luo H, Baum JD, Löhner R (2006) A hybrid Cartesian grid and grid less method for compressible flows. J Comput Phys 214:618–632. Scholar
  20. Mittal R, Iaccarino G (2005) Immersed boundary methods. Annu Rev Fluid Mech 37:239–261. Scholar
  21. Mizuno Y, Takahashi S, Nonomura T, Nagata T, Fukuda K (2015) A simple immersed boundary method for compressible flow simulation around a stationary and moving sphere. Math Probl Eng 2015:1–17. Scholar
  22. Mo H, Lien FS, Zhang F, Cornin DS (2016) A sharp interface immersed boundary method for solving flow with arbitrarily irregular and changing geometry. Phys Fluid Dyn. eprint arXiv:1602.06830
  23. Natarajan G (2009) Residual error estimation and adaptive algorithms for fluid flows. Ph.D. thesis dissertation, Indian Institute of Science, BangaloreGoogle Scholar
  24. Ni RH (1982) A multiple-grid scheme for solving the Euler equations. AIAA J 20:1565–1571. Scholar
  25. Palma PD, de Tullio MD, Pascazio G, Napolitano M (2006) An immersed boundary method for compressible viscous flows. Comp Fluids 35:693–702. Scholar
  26. Peskin CS (1972) Flow patters around heart valves: a numerical method. J Comput Phys 10:252–271. Scholar
  27. Pu TM, Zhou CH (2018) An immersed boundary/wall modeling method for RANS simulation of compressible turbulent flows. Int J Numer Methods Fluids 87:217–238. Scholar
  28. Qu Y, Shi R, Batra RC (2018) An immersed boundary formulation for simulating high-speed compressible viscous flows with moving solids. J Comput Phys 354:672–691. Scholar
  29. Sambasivan SK, UdayKumar H (2009) Ghost fluid method for strong shock interactions part 2: Immersed solid boundaries. AIAA J 47:2923–2937. Scholar
  30. Sambasivan SK, UdayKumar HS (2010) Sharp interface simulations with local mesh refinement for multi-material dynamics in strongly shocked flows. Comp Fluids 39:1456–1479. Scholar
  31. Sekhar S, Ruffin SM (2013) Predictions of convective heat transfer rates using a Cartesian grid solver for hypersonic flows. In: 44th AIAA thermophysics conference, San Diego, CA.
  32. Sotiropoulos F, Yang X (2014) Immersed boundary methods for simulating fluid-structure interaction. Prog Aero Sci 65:1–21. Scholar
  33. Sridar D, Balakrishnan N (2003) An upwind finite difference scheme for mesh less solvers. J Comput Phys 189:1–29. Scholar
  34. Udaykumar HS, Shyy W (1995) Simulation of inter facial instabilities during solidification—I. Conduction and capillarity effects. Int J Heat Mass Transf 38:2057–2073. Scholar
  35. Wieting AR (1987) Experimental study of shock wave interface heating on a cylindrical leading edge. NASA TM-100484Google Scholar
  36. Ye T, Mittal R, Udaykumar HS, Shyy W (1999) An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. J Comput Phys 156:209–240. Scholar
  37. Zhang Y, Zhou CH (2014) An immersed boundary method for simulation of inviscid compressible flows. Int J Numer Methods Fluids 74:775–793. Scholar
  38. Zhao H, Hu P, Kamakoti R, Dittakavi N, Xue L, Ni K, Mao S, Marshall DD, Aftosmis M (2010) Towards efficient viscous modeling based on Cartesian methods for automated flow simulation. In: 48th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, Orlando, Florida, (2010).

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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Indian Institute of Technology GuwahatiGuwahatiIndia
  2. 2.Indian Institute of Technology PalakkadPalakkadIndia

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