Application of Novel Conserving Immersed Boundary Method to Moving Boundary Problem
A new conserving approach in the context of Immersed Boundary Method (IBM) is presented to simulate one dimensional, incompressible flow in a moving boundary problem. The method employs control volume scheme to simulate the flow field. The concept of ghost node is used at the boundaries to conserve the mass and momentum equations. The Present method implements the conservation laws in all cells including boundary control volumes. Application of the method is studied in a test case with moving boundary. Comparison between the results of this new method and a sharp interface (Image Point Method) IBM algorithm shows a well distinguished improvement in both pressure and velocity fields of the present method. Fluctuations in pressure field are fully resolved in this proposed method. This approach expands the IBM capability to simulate flow field for variety of problems by implementing conservation laws in a fully Cartesian grid compared to other conserving methods.
[1] Peskin, C. S. Flow patterns around heart valves: A numerical method.
Computational Physics, v. 10, p. 252-71, 1972. Peskin, C. S. The fluid dynamics of heart valves: experimental, theoretical and computational methods. Annual Review. Fluid
Mechanic, v. 14, p. 235-59, 1981.
[2] Berger, M.; Aftosmis, M. Aspects (and aspect ratios) of cartesian mesh
methods. (S.l.): Proc. 16th Int. Conf. Numerical Methods Fluid. 1998.
[3] Lai, M.; Peskin, C. An immersed boundary method with formal secondorder
accuracy and reduced numerical viscosity. Computational Physics,
v. 160, p. 705-19, 2000.
[4] Saiki, E.; Biringen, S. Numerical simulation of a cylinder in uniform
flow: application of a virtual boundary method, v. 123, p. 450-65, 1996.
[5] Goldstein, D.; Handler, R.; Sirovich, L. Modeling a no-slip
flowboundary with an external force field. Computational Physics, v.
105, p. 354-66, 1993.
[6] Iaccarino, G.; Verzicco, R. Immersed boundary technique for turbulent
flow simulations. Mechanical Review, v. 56, p. 331-47, 2003.
[7] Angot, P.; Bruneau, C.; Frabrie, P. Apenalization method to take into
account obstacles in viscous flows. Numericall Mathematics, v. 81, p.
497-520, 1999.
[8] Khadra, K. et al. Fictitious domain approach for numerical modeling of
Navier-Stokes equations. Numerical Methods Fluids, v. 34, p. 651-84,
2000.
[9] Majumdar, S.; Iaccarino, G.; Durbin, P. Rans solver with adaptive
structured boundary non-conforming grids. Cent. Turbul. Res. , n. 2001,
, p. 353-64, 2001.
[10] Ghias, R.; Mittal, R.; Lund, T. A non-body conformal grid method for
simulation of compressible flows with complex immersed boundaries.
AIAA, p. 2004-0080, 2004.
[11] Ghias, R.; Mittal, R.; Dong, H. A sharp interface immersed boundary
method for compressible viscous flows. computational phusics, v. 225,
p. 528-53, 2007.
[12] Clarke, D.; M., S.; H., H. Euler calculations for multi-element airfoils
using Cartesian grids. AIAA, v. 24, p. 1128-35, 1986.
[13] Zeeuw, D.; Powell, K. An adaptively refined cartesian mesh solver for
the Euler equations. AIAA, v. 1991-1542, 1991.
[14] Udaykumar, H.; Shyy, W.; Rao, M. Elafint: A mixed Eulerian-
Lagrangian method for fluid flows with complex and moving
boundaries. Numerical Methods, v. 22, p. 691-705, 1996.
[15] Udaykumar, H. et al. A sharp interface cartesian grid method for
simulating flows with complex moving boundaries. computational
physics, v. 174, p. 345-80, 2001.
[16] Udaykumar, H.; Mittal, R.; Rampunggoon. Interface tracking finite
volume method for complex solid-fluid interactions on fixed meshes.
Commun. Numerical Methods Engineering, v. 18, p. 89-97, 2002.
[17] Ye, T. et al. An accurate cartesian grid method for viscous
incompressible flows with complex immersed boundaries.
Computational Physics, v. 156, p. 209-40, 1999.
[18] Karimian, S. M. H.; Amoli, A.; Mazaheri, K. Control-volume finiteelement
method for the solution of 2D euler equations on unstructured
moving grids. Iranian Journal of Science & Technology, v. 26, p. 465-76
, 2002.
[19] Karimian, S. M. H.; Schneider, G. E. Pressure-Based comptational
method for compressible and incompressibleflows. AIAA, Journal of
Thermodynamics and heat transfer, v. 8, p. 267-74, 1994.
[20] Mittal, R.; Iaccarino, G. Immersed Boundary Methods. Fluid Mechanics
, v. 37, p. 239-61, 2005.
[1] Peskin, C. S. Flow patterns around heart valves: A numerical method.
Computational Physics, v. 10, p. 252-71, 1972. Peskin, C. S. The fluid dynamics of heart valves: experimental, theoretical and computational methods. Annual Review. Fluid
Mechanic, v. 14, p. 235-59, 1981.
[2] Berger, M.; Aftosmis, M. Aspects (and aspect ratios) of cartesian mesh
methods. (S.l.): Proc. 16th Int. Conf. Numerical Methods Fluid. 1998.
[3] Lai, M.; Peskin, C. An immersed boundary method with formal secondorder
accuracy and reduced numerical viscosity. Computational Physics,
v. 160, p. 705-19, 2000.
[4] Saiki, E.; Biringen, S. Numerical simulation of a cylinder in uniform
flow: application of a virtual boundary method, v. 123, p. 450-65, 1996.
[5] Goldstein, D.; Handler, R.; Sirovich, L. Modeling a no-slip
flowboundary with an external force field. Computational Physics, v.
105, p. 354-66, 1993.
[6] Iaccarino, G.; Verzicco, R. Immersed boundary technique for turbulent
flow simulations. Mechanical Review, v. 56, p. 331-47, 2003.
[7] Angot, P.; Bruneau, C.; Frabrie, P. Apenalization method to take into
account obstacles in viscous flows. Numericall Mathematics, v. 81, p.
497-520, 1999.
[8] Khadra, K. et al. Fictitious domain approach for numerical modeling of
Navier-Stokes equations. Numerical Methods Fluids, v. 34, p. 651-84,
2000.
[9] Majumdar, S.; Iaccarino, G.; Durbin, P. Rans solver with adaptive
structured boundary non-conforming grids. Cent. Turbul. Res. , n. 2001,
, p. 353-64, 2001.
[10] Ghias, R.; Mittal, R.; Lund, T. A non-body conformal grid method for
simulation of compressible flows with complex immersed boundaries.
AIAA, p. 2004-0080, 2004.
[11] Ghias, R.; Mittal, R.; Dong, H. A sharp interface immersed boundary
method for compressible viscous flows. computational phusics, v. 225,
p. 528-53, 2007.
[12] Clarke, D.; M., S.; H., H. Euler calculations for multi-element airfoils
using Cartesian grids. AIAA, v. 24, p. 1128-35, 1986.
[13] Zeeuw, D.; Powell, K. An adaptively refined cartesian mesh solver for
the Euler equations. AIAA, v. 1991-1542, 1991.
[14] Udaykumar, H.; Shyy, W.; Rao, M. Elafint: A mixed Eulerian-
Lagrangian method for fluid flows with complex and moving
boundaries. Numerical Methods, v. 22, p. 691-705, 1996.
[15] Udaykumar, H. et al. A sharp interface cartesian grid method for
simulating flows with complex moving boundaries. computational
physics, v. 174, p. 345-80, 2001.
[16] Udaykumar, H.; Mittal, R.; Rampunggoon. Interface tracking finite
volume method for complex solid-fluid interactions on fixed meshes.
Commun. Numerical Methods Engineering, v. 18, p. 89-97, 2002.
[17] Ye, T. et al. An accurate cartesian grid method for viscous
incompressible flows with complex immersed boundaries.
Computational Physics, v. 156, p. 209-40, 1999.
[18] Karimian, S. M. H.; Amoli, A.; Mazaheri, K. Control-volume finiteelement
method for the solution of 2D euler equations on unstructured
moving grids. Iranian Journal of Science & Technology, v. 26, p. 465-76
, 2002.
[19] Karimian, S. M. H.; Schneider, G. E. Pressure-Based comptational
method for compressible and incompressibleflows. AIAA, Journal of
Thermodynamics and heat transfer, v. 8, p. 267-74, 1994.
[20] Mittal, R.; Iaccarino, G. Immersed Boundary Methods. Fluid Mechanics
, v. 37, p. 239-61, 2005.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56635", author = "S. N. Hosseini and S. M. H. Karimian", title = "Application of Novel Conserving Immersed Boundary Method to Moving Boundary Problem", abstract = "A new conserving approach in the context of Immersed Boundary Method (IBM) is presented to simulate one dimensional, incompressible flow in a moving boundary problem. The method employs control volume scheme to simulate the flow field. The concept of ghost node is used at the boundaries to conserve the mass and momentum equations. The Present method implements the conservation laws in all cells including boundary control volumes. Application of the method is studied in a test case with moving boundary. Comparison between the results of this new method and a sharp interface (Image Point Method) IBM algorithm shows a well distinguished improvement in both pressure and velocity fields of the present method. Fluctuations in pressure field are fully resolved in this proposed method. This approach expands the IBM capability to simulate flow field for variety of problems by implementing conservation laws in a fully Cartesian grid compared to other conserving methods.
", keywords = "Immersed Boundary Method, conservation of mass and momentum laws, moving boundary, boundary condition.", volume = "7", number = "4", pages = "597-8", }
