An improved immersed boundary method for curvilinear grids

Enrico Napoli, Roman, Armenio

Risultato della ricerca: Article

53 Citazioni (Scopus)

Abstract

In the present paper we propose an extension of the direct-forcing immersed boundary technique, recently developed and employed by Verzicco and co-authors [Fadlun EA, Verzicco R, Orlandi P, Mohd-Yusof J. Combined immersed-boundary finite-difference methods for three-dimensional complex flowsimulations. J Comput Phys 2000;161:35–60; Verzicco R, Fatica M, Iaccarino G, Moin P, Khalighi B. Large eddy simulation of a road vehicle with drag-reduction devices. AIAA J 2002;40(12):2447–55; Cristallo A, Verzicco R. Combined immersed boundary/large-eddy-simulations of incompressible three-dimensional complex flows. Flow Turbul Combust 2006;77(1–4):3–26.] and successively improved by Balaras and coauthors [Gilmanov A, Sotiropoulos F, Balaras E. A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids. J Comput Phys 003;191:660–9; Balaras E. Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddysimulations. Comput Fluids 2004;33:375–404]. We extend the aforementioned technique to curvilinear-coordinate, structured grid, Navier–Stokes solvers. This improved technique allows for more flexibility and efficiency when compared to standard methods in which the technique is coupled withorthogonal-grid solvers. Additional modifications are also proposed with respect to the state-of-art, which allow to deal with general shaped, multiple-body immersed surfaces and to make the interpolationof the velocity field off the body suitable for curvilinear grids. Several tests have been carried out to check the reliability of the proposed technique: first we have considered the three-dimensional Stokesflow around a sphere, and compared the numerical results with the analytical ones. Second we have considered the two-dimensional unsteady flow around a circular cylinder placed between two parallel solid walls and compared the results with those of the database of the Priority Research Program ‘FlowSimulation on High Performance Computers’ of the German Research Association (DFG). Third, we have considered the two-dimensional flow within a S-shaped duct containing an elliptical valve. Finally, wehave applied the technique to the study of a practical high-Reynolds number industrial problem.The geometrical configuration of the first two test cases is suited for both Cartesian and curvilinear algorithms. The geometry of the third test case is suited for curvilinear meshes and makes the use ofCartesian grids very inefficient and less accurate than the curvilinear ones. In these cases Cartesian – as well as curvilinear – mesh simulations have been carried out. Finally, the geometry of the high-Reynoldsindustrial problem is suited for curvilinear grids.The proposed technique has shown to preserve at least the same level of accuracy of its Cartesian counterpart allowing to reduce in a considerable way the computational cost of the simulations. When the geometry is better suited for curvilinear meshes, the reduction of the computational cost is accompaniedby an increased accuracy with respect to the Cartesian counterpart. We also propose a simplified direct-forcing, semi-implicit method, allowing reduced computational cost with respect to the literature techniques. We have checked the accuracy of the technique and shownthat when the Reynolds number is large enough, the present simplified technique allows the use of time steps much larger than those allowed by the explicit time-advancement scheme, preserving the accuracy of the results.
Lingua originaleEnglish
pagine (da-a)1510-1527
Numero di pagine18
RivistaDefault journal
Volume38
Stato di pubblicazionePublished - 2009

Fingerprint

Large eddy simulation
Geometry
Reynolds number
Costs
Drag reduction
Unsteady flow
Circular cylinders
Finite difference method
Ducts
Fluids

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Engineering(all)

Cita questo

An improved immersed boundary method for curvilinear grids. / Napoli, Enrico; Roman; Armenio.

In: Default journal, Vol. 38, 2009, pag. 1510-1527.

Risultato della ricerca: Article

Napoli, E, Roman & Armenio 2009, 'An improved immersed boundary method for curvilinear grids', Default journal, vol. 38, pagg. 1510-1527.
Napoli, Enrico ; Roman ; Armenio. / An improved immersed boundary method for curvilinear grids. In: Default journal. 2009 ; Vol. 38. pagg. 1510-1527.
@article{d1dc7fe039cc4e2299905c2208066eb2,
title = "An improved immersed boundary method for curvilinear grids",
abstract = "In the present paper we propose an extension of the direct-forcing immersed boundary technique, recently developed and employed by Verzicco and co-authors [Fadlun EA, Verzicco R, Orlandi P, Mohd-Yusof J. Combined immersed-boundary finite-difference methods for three-dimensional complex flowsimulations. J Comput Phys 2000;161:35–60; Verzicco R, Fatica M, Iaccarino G, Moin P, Khalighi B. Large eddy simulation of a road vehicle with drag-reduction devices. AIAA J 2002;40(12):2447–55; Cristallo A, Verzicco R. Combined immersed boundary/large-eddy-simulations of incompressible three-dimensional complex flows. Flow Turbul Combust 2006;77(1–4):3–26.] and successively improved by Balaras and coauthors [Gilmanov A, Sotiropoulos F, Balaras E. A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids. J Comput Phys 003;191:660–9; Balaras E. Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddysimulations. Comput Fluids 2004;33:375–404]. We extend the aforementioned technique to curvilinear-coordinate, structured grid, Navier–Stokes solvers. This improved technique allows for more flexibility and efficiency when compared to standard methods in which the technique is coupled withorthogonal-grid solvers. Additional modifications are also proposed with respect to the state-of-art, which allow to deal with general shaped, multiple-body immersed surfaces and to make the interpolationof the velocity field off the body suitable for curvilinear grids. Several tests have been carried out to check the reliability of the proposed technique: first we have considered the three-dimensional Stokesflow around a sphere, and compared the numerical results with the analytical ones. Second we have considered the two-dimensional unsteady flow around a circular cylinder placed between two parallel solid walls and compared the results with those of the database of the Priority Research Program ‘FlowSimulation on High Performance Computers’ of the German Research Association (DFG). Third, we have considered the two-dimensional flow within a S-shaped duct containing an elliptical valve. Finally, wehave applied the technique to the study of a practical high-Reynolds number industrial problem.The geometrical configuration of the first two test cases is suited for both Cartesian and curvilinear algorithms. The geometry of the third test case is suited for curvilinear meshes and makes the use ofCartesian grids very inefficient and less accurate than the curvilinear ones. In these cases Cartesian – as well as curvilinear – mesh simulations have been carried out. Finally, the geometry of the high-Reynoldsindustrial problem is suited for curvilinear grids.The proposed technique has shown to preserve at least the same level of accuracy of its Cartesian counterpart allowing to reduce in a considerable way the computational cost of the simulations. When the geometry is better suited for curvilinear meshes, the reduction of the computational cost is accompaniedby an increased accuracy with respect to the Cartesian counterpart. We also propose a simplified direct-forcing, semi-implicit method, allowing reduced computational cost with respect to the literature techniques. We have checked the accuracy of the technique and shownthat when the Reynolds number is large enough, the present simplified technique allows the use of time steps much larger than those allowed by the explicit time-advancement scheme, preserving the accuracy of the results.",
keywords = "Curvilinear grid, Immersed boundary, Numerical methods",
author = "Enrico Napoli and Roman and Armenio",
year = "2009",
language = "English",
volume = "38",
pages = "1510--1527",
journal = "Default journal",

}

TY - JOUR

T1 - An improved immersed boundary method for curvilinear grids

AU - Napoli, Enrico

AU - Roman, null

AU - Armenio, null

PY - 2009

Y1 - 2009

N2 - In the present paper we propose an extension of the direct-forcing immersed boundary technique, recently developed and employed by Verzicco and co-authors [Fadlun EA, Verzicco R, Orlandi P, Mohd-Yusof J. Combined immersed-boundary finite-difference methods for three-dimensional complex flowsimulations. J Comput Phys 2000;161:35–60; Verzicco R, Fatica M, Iaccarino G, Moin P, Khalighi B. Large eddy simulation of a road vehicle with drag-reduction devices. AIAA J 2002;40(12):2447–55; Cristallo A, Verzicco R. Combined immersed boundary/large-eddy-simulations of incompressible three-dimensional complex flows. Flow Turbul Combust 2006;77(1–4):3–26.] and successively improved by Balaras and coauthors [Gilmanov A, Sotiropoulos F, Balaras E. A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids. J Comput Phys 003;191:660–9; Balaras E. Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddysimulations. Comput Fluids 2004;33:375–404]. We extend the aforementioned technique to curvilinear-coordinate, structured grid, Navier–Stokes solvers. This improved technique allows for more flexibility and efficiency when compared to standard methods in which the technique is coupled withorthogonal-grid solvers. Additional modifications are also proposed with respect to the state-of-art, which allow to deal with general shaped, multiple-body immersed surfaces and to make the interpolationof the velocity field off the body suitable for curvilinear grids. Several tests have been carried out to check the reliability of the proposed technique: first we have considered the three-dimensional Stokesflow around a sphere, and compared the numerical results with the analytical ones. Second we have considered the two-dimensional unsteady flow around a circular cylinder placed between two parallel solid walls and compared the results with those of the database of the Priority Research Program ‘FlowSimulation on High Performance Computers’ of the German Research Association (DFG). Third, we have considered the two-dimensional flow within a S-shaped duct containing an elliptical valve. Finally, wehave applied the technique to the study of a practical high-Reynolds number industrial problem.The geometrical configuration of the first two test cases is suited for both Cartesian and curvilinear algorithms. The geometry of the third test case is suited for curvilinear meshes and makes the use ofCartesian grids very inefficient and less accurate than the curvilinear ones. In these cases Cartesian – as well as curvilinear – mesh simulations have been carried out. Finally, the geometry of the high-Reynoldsindustrial problem is suited for curvilinear grids.The proposed technique has shown to preserve at least the same level of accuracy of its Cartesian counterpart allowing to reduce in a considerable way the computational cost of the simulations. When the geometry is better suited for curvilinear meshes, the reduction of the computational cost is accompaniedby an increased accuracy with respect to the Cartesian counterpart. We also propose a simplified direct-forcing, semi-implicit method, allowing reduced computational cost with respect to the literature techniques. We have checked the accuracy of the technique and shownthat when the Reynolds number is large enough, the present simplified technique allows the use of time steps much larger than those allowed by the explicit time-advancement scheme, preserving the accuracy of the results.

AB - In the present paper we propose an extension of the direct-forcing immersed boundary technique, recently developed and employed by Verzicco and co-authors [Fadlun EA, Verzicco R, Orlandi P, Mohd-Yusof J. Combined immersed-boundary finite-difference methods for three-dimensional complex flowsimulations. J Comput Phys 2000;161:35–60; Verzicco R, Fatica M, Iaccarino G, Moin P, Khalighi B. Large eddy simulation of a road vehicle with drag-reduction devices. AIAA J 2002;40(12):2447–55; Cristallo A, Verzicco R. Combined immersed boundary/large-eddy-simulations of incompressible three-dimensional complex flows. Flow Turbul Combust 2006;77(1–4):3–26.] and successively improved by Balaras and coauthors [Gilmanov A, Sotiropoulos F, Balaras E. A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids. J Comput Phys 003;191:660–9; Balaras E. Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddysimulations. Comput Fluids 2004;33:375–404]. We extend the aforementioned technique to curvilinear-coordinate, structured grid, Navier–Stokes solvers. This improved technique allows for more flexibility and efficiency when compared to standard methods in which the technique is coupled withorthogonal-grid solvers. Additional modifications are also proposed with respect to the state-of-art, which allow to deal with general shaped, multiple-body immersed surfaces and to make the interpolationof the velocity field off the body suitable for curvilinear grids. Several tests have been carried out to check the reliability of the proposed technique: first we have considered the three-dimensional Stokesflow around a sphere, and compared the numerical results with the analytical ones. Second we have considered the two-dimensional unsteady flow around a circular cylinder placed between two parallel solid walls and compared the results with those of the database of the Priority Research Program ‘FlowSimulation on High Performance Computers’ of the German Research Association (DFG). Third, we have considered the two-dimensional flow within a S-shaped duct containing an elliptical valve. Finally, wehave applied the technique to the study of a practical high-Reynolds number industrial problem.The geometrical configuration of the first two test cases is suited for both Cartesian and curvilinear algorithms. The geometry of the third test case is suited for curvilinear meshes and makes the use ofCartesian grids very inefficient and less accurate than the curvilinear ones. In these cases Cartesian – as well as curvilinear – mesh simulations have been carried out. Finally, the geometry of the high-Reynoldsindustrial problem is suited for curvilinear grids.The proposed technique has shown to preserve at least the same level of accuracy of its Cartesian counterpart allowing to reduce in a considerable way the computational cost of the simulations. When the geometry is better suited for curvilinear meshes, the reduction of the computational cost is accompaniedby an increased accuracy with respect to the Cartesian counterpart. We also propose a simplified direct-forcing, semi-implicit method, allowing reduced computational cost with respect to the literature techniques. We have checked the accuracy of the technique and shownthat when the Reynolds number is large enough, the present simplified technique allows the use of time steps much larger than those allowed by the explicit time-advancement scheme, preserving the accuracy of the results.

KW - Curvilinear grid

KW - Immersed boundary

KW - Numerical methods

UR - http://hdl.handle.net/10447/47747

M3 - Article

VL - 38

SP - 1510

EP - 1527

JO - Default journal

JF - Default journal

ER -