A Hybrid Mesh Free Local RBF- Cartesian FD Scheme for Incompressible Flow around Solid Bodies
References:
[1] S. Dennis, and G.-Z. Chang, “Numerical solutions for steady flow past a
circular cylinder at Reynolds numbers up to 100,” J. Fluid Mech, vol.
42, no. 3, pp. 471-489, 1970.
[2] M. Braza, P. Chassaing, and H. H. Minh, “Numerical Study and
Physical Analysis of the Pressure and Velocity-Fields in the near Wake of a Circular-Cylinder,” Journal of Fluid Mechanics, vol. 165, pp. 79-
130, Apr, 1986.
[3] H. Takami, and H. B. Keller, “Steady Two‐Dimensional Viscous Flow
of an Incompressible Fluid past a Circular Cylinder,” Physics of Fluids,
vol. 12, no. 12, pp. II-51-II-56, 1969.
[4] L. B. Lucy, “A numerical approach to the testing of fission hypothesis,”
Astronomical Journal, vol. 8, pp. 1013-1024, 1977.
[5] B. Nayroles, G. Touzot, and P. Villon, “Generalizing the finite element
method: Diffuse approximation and diffuse elements,” Computational
Mechanics, vol. 10, no. 5, pp. 307-318, 1992.
[6] T. Belytschko, Y. Y. Lu, and L. Gu, “ELEMENT-FREE GALERKIN
METHODS,” International Journal for Numerical Methods in
Engineering, vol. 37, no. 2, pp. 229-256, 1994.
[7] W. K. Liu, S. Jun, S. F. Li, J. Adee, and T. Belytschko, “Reproducing
Kernel Particle Methods for Structural Dynamics,” International
Journal for Numerical Methods in Engineering, vol. 38, no. 10, pp.
1655-1679, May 30, 1995.
[8] J. M. Melenk, and I. Babuska, “The partition of unity finite element
method: Basic theory and applications,” Computer Methods in Applied
Mechanics and Engineering, vol. 139, no. 1-4, pp. 289-314, Dec 15,
1996.
[9] E. Onate, S. Idelsohn, O. C. Zienkiewicz, R. L. Taylor, and C. Sacco, “A
stabilized finite point method for analysis of fluid mechanics problems,”
Computer Methods in Applied Mechanics and Engineering, vol. 139, no.
1-4, pp. 315-346, Dec 15, 1996.
[10] C. Liu, X. Zheng, and C. Sung, “Preconditioned multigrid methods for
unsteady incompressible flows,” Journal of Computational Physics, vol.
139, no. 1, pp. 35-57, 1998.
[11] H. Ding, C. Shu, K. S. Yeo, and D. Xu, “Simulation of incompressible
viscous flows past a circular cylinder by hybrid FD scheme and
meshless least square-based finite difference method,” Computer
Methods in Applied Mechanics and Engineering, vol. 193, no. 9-11, pp.
727-744, 2004.
[12] Y. Sanyasiraju, and G. Chandhini, “Local radial basis function based
gridfree scheme for unsteady incompressible viscous flows,” Journal of
Computational Physics, vol. 227, no. 20, pp. 8922-8948, Oct, 2008.
[13] J. P. Morris, P. J. Fox, and Y. Zhu, “Modeling low Reynolds number
incompressible flows using SPH,” Journal of Computational Physics,
vol. 136, no. 1, pp. 214-226, Sep 1, 1997.
[14] J. J. Monaghan, “Simulating Free-Surface Flows with Sph,” Journal of
Computational Physics, vol. 110, no. 2, pp. 399-406, Feb, 1994.
[15] M. B. Liu, G. R. Liu, and K. Y. Lam, “Constructing smoothing functions
in smoothed particle hydrodynamics with applications,” Journal of
Computational and Applied Mathematics, vol. 155, no. 2, pp. 263-284,
Jun 15, 2003.
[16] M. Liu, G. Liu, Z. Zong, and K. Lam, "Numerical simulation of
incompressible flows by SPH."
[17] C. Shu, H. Ding., and K. S. Yeo., “Computation of Incompressible
Navier-Stokes Equations by Local RBF-based Differential Quadrature
Method,” Computer Modeling in Engineering and Sciences, vol. 7, no.
2, pp. 195-206, 2005.
[18] C. Shu, H. Ding, and K. S. Yeo, “Local radial basis function-based
differential quadrature method and its application to solve twodimensional
incompressible Navier-Stokes equations,” Computer
Methods in Applied Mechanics and Engineering, vol. 192, no. 7-8, pp.
941-954, 2003.
[19] C. G. Koh, M. Gao, and C. Luo, “A new particle method for simulation
of incompressible free surface flow problems,” International Journal for
Numerical Methods in Engineering, vol. 89, no. 12, pp. 1582-1604, Mar
23, 2012.
[20] S.-y. Tuann, and M. D. Olson, “Numerical studies of the flow around a
circular cylinder by a finite element method,” Computers & Fluids, vol.
6, no. 4, pp. 219-240, 12//, 1978.
[21] C. S. Chew, K. S. Yeo, and C. Shu, “A generalized finite-difference
(GFD) ALE scheme for incompressible flows around moving solid
bodies on hybrid meshfree–Cartesian grids,” Journal of Computational
Physics, vol. 218, no. 2, pp. 510-548, 11/1/, 2006.
[22] A. Belov, L. Martinelli, and A. Jameson, “A new implicit algorithm with
multigrid for unsteady incompressible flow calculations,” AIAA paper,
vol. 95, pp. 0049, 1995.
[23] X. He, and G. Doolen, “Lattice Boltzmann method on curvilinear
coordinates system: flow around a circular cylinder,” Journal of
Computational Physics, vol. 134, no. 2, pp. 306-315, 1997.
[24] R. Mei, and W. Shyy, “On the finite difference-based lattice Boltzmann
method in curvilinear coordinates,” Journal of Computational Physics,
vol. 143, no. 2, pp. 426-448, 1998.
[25] E. J. Kansa, “Multiquadrics - a Scattered Data Approximation Scheme
with Applications to Computational Fluid-Dynamics .2. Solutions to
Parabolic, Hyperbolic and Elliptic Partial-Differential Equations,”
Computers & Mathematics with Applications, vol. 19, no. 8-9, pp. 147-
161, 1990.
[26] J. G. Wang, and G. R. Liu, “On the optimal shape parameters of radial
basis functions used for 2-D meshless methods,” Computer Methods in
Applied Mechanics and Engineering, vol. 191, no. 23-24, pp. 2611-
2630, 2002.
[27] P. P. Chinchapatnam, K. Djidjeli, and P. B. Nair, “Radial basis function
meshless method for the steady incompressible Navier–Stokes
equations,” International Journal of Computer Mathematics, vol. 84, no.
10, pp. 1509-1521, 2007.
[28] Z. Guo, B. Shi, and N. Wang, “Lattice BGK model for incompressible
Navier–Stokes equation,” Journal of Computational Physics, vol. 165,
no. 1, pp. 288-306, 2000.
[29] A. I. Tolstykh, and D. A. Shirobokov, “On using radial basis functions
in a "finite difference mode" with applications to elasticity problems,”
Computational Mechanics, vol. 33, no. 1, pp. 68-79, Dec, 2003.
[30] G. B. Wright, and B. Fornberg, “Scattered node compact finite
difference-type formulas generated from radial basis functions,” Journal
of Computational Physics, vol. 212, no. 1, pp. 99-123, Feb 10, 2006.
[31] A. R. Firoozjaee, and M. H. Afshar, “Steady-state solution of
incompressible Navier–Stokes equations using discrete least-squares
meshless method,” International Journal for Numerical Methods in
Fluids, vol. 67, no. 3, pp. 369-382, 2011.
[32] P. P. Chinchapatnam, K. Djidjeli, P. B. Nair, and M. Tan, “A compact
RBF-FD based meshless method for the incompressible Navier-Stokes
equations,” Proceedings of the Institution of Mechanical Engineers Part
M-Journal of Engineering for the Maritime Environment, vol. 223, no.
M3, pp. 275-290, Aug, 2009.
[33] C. Perng, and R. Street, “A coupled multigrid‐domain‐splitting
technique for simulating incompressible flows in geometrically complex
domains,” International journal for numerical methods in fluids, vol. 13,
no. 3, pp. 269-286, 1991.
[34] M. Hinatsu, and J. Ferziger, “Numerical computation of unsteady
incompressible flow in complex geometry using a composite multigrid
technique,” International Journal for Numerical Methods in Fluids, vol.
13, no. 8, pp. 971-997, 1991.
[35] P. Chow, and C. Addison, “Putting domain decomposition at the heart of
a mesh‐based simulation process,” International journal for numerical
methods in fluids, vol. 40, no. 12, pp. 1471-1484, 2002.
[36] D. Calhoun, “A Cartesian grid method for solving the two-dimensional
streamfunction-vorticity equations in irregular regions,” Journal of
Computational Physics, vol. 176, no. 2, pp. 231-275, 2002.
[37] R. B. Pember, J. B. Bell, P. Colella, W. Y. Curtchfield, and M. L.
Welcome, “An adaptive Cartesian grid method for unsteady
compressible flow in irregular regions,” Journal of computational
Physics, vol. 120, no. 2, pp. 278-304, 1995.
[38] J. Falcovitz, G. Alfandary, and G. Hanoch, “A two-dimensional
conservation laws scheme for compressible flows with moving
boundaries,” Journal of Computational Physics, vol. 138, no. 1, pp. 83-
102, 1997.
[39] A. Gilmanov, F. Sotiropoulos, and E. Balaras, “A general reconstruction
algorithm for simulating flows with complex 3D immersed boundaries
on Cartesian grids,” Journal of Computational Physics, vol. 191, no. 2,
pp. 660-669, 2003.
[40] R. Glowinski, T.-W. Pan, and J. Periaux, “A fictitious domain method
for external incompressible viscous flow modeled by Navier-Stokes
equations,” Computer Methods in Applied Mechanics and Engineering,
vol. 112, no. 1, pp. 133-148, 1994.
[41] A. Javed, K. Djidjeli, and J. Xing, Tang, “Shape adaptive RBF-FD
Implicit Scheme for Incompressible Viscous Navier-Strokes Equations,”
Journal of Computer and Fluid, vol. submitted for Publication, 2013.
[42] J. Kim, and P. Moin, “Application of a Fractional-Step Method to
Incompressible Navier-Stokes Equations,” Journal of Computational
Physics, vol. 59, no. 2, pp. 308-323, June, 1985, 1985.
[43] B. Fornberg, “A Numerical Study of Steady Viscous-Flow Past a
Circular-Cylinder,” Journal of Fluid Mechanics, vol. 98, no. Jun, pp.
819-855, 1980.
[44] D. Kim, and H. Choi, “A second-order time-accurate finite volume
method for unsteady incompressible flow on hybrid unstructured grids,”
Journal of Computational Physics, vol. 162, no. 2, pp. 411-428, 2000.
[45] Y. Zang, R. L. Street, and J. R. Koseff, “A non-staggered grid, fractional
step method for time-dependent incompressible Navier-Stokes equations
in curvilinear coordinates,” Journal of Computational Physics, vol. 114,
no. 1, pp. 18-33, 1994.