شبیه‌سازی حرکت جسم جامد در یک سیال نیوتونی با استفاده از یک روش مرزمستور شبه‌طیفی موازی‌شده تاوایی‌مبنا

1. Razaghi, M., “A Smart Computational Grid Around a Three-dimensional Moving Body”, Fluid Mechanics and Aerodynamics Journal, Vol. 7, No. 2, pp. 73-88, 2019.##
2. Griffith, B. E. and Peskin, C. S., “On The Order of Accuracy of the Immersed Boundary Method: Higher order convergence rates for sufficiently smooth problems”, J. Comput. Phys., Vol. 208, No. 75, 2005.##
3. Taira, K. and Colonius, K. “The Mmmersed Boundary Method: a Projection Approach”, J. Comput. Phys., Vol. 225, No. 2, pp. 2118-2137, 2007.##
4. Fadlun, E. A., Verzicco, R., Orlandi, P., and Mohd-Yusofz, J. “Combined Immersed-Boundary Finite-difference Methods for Three-dimensional Complex Flow Simulations J. Comput. Phys., Vol. 161, pp.35–60, 2000.##
5. Vanella, M. ,Rabenold, P., and Balaras, E., “A Direct-forcing Embedded-boundary Method with Adaptive Mesh Refinement for Fluid–Structure Interaction Problems”, J. Comput. Phys., Vol. 229 (18), pp. 6427 – 6449, 2010.##
6. Mittal, R., and Iaccarino, G. “Immersed Boundary Methods”, Annu. Rev. Fluid Mech., Vol. 3, pp. 239-261, 2005.##
7. Russell, D. and Jane Wang, Z., “A Cartesian Grid Method for Modeling Multiple Moving Objects in 2D Incompressible Viscous Flow”, J. Comput. Phys., Vol. 191, pp. 177–205, 2003.##
8. Keetels, G. H., D’Ortona, U., Kramer, W., Clercx, H. J. H., Schneider, K., and Van Heijst, G. J. F. “Fourier Spectral and Wavelet Solvers for The Incompressible Navier–Stokes Equations With Volume-penalization: Convergence of a Dipole–wall Collision”, J. Comput. Phys., Vol. 227, pp. 919–945, 2007.##
9. Calhoun, D. “A Cartesian Grid Method for Solving The Streamfunction-vorticity Equations in Irregular Geometries,” PhD. Dissertation, University of Washington, 1999.##
10. Kolomenskiy, D. and Schneider, K. “A Fourier Spectral Method for The Navier–Stokes Equations With Volume Penalization for Moving Solid Obstacles”, J. Comput. Phys., Vol. 228, pp. 5687–5709, 2009.##
11. Wang, Z., Fan, J., and Cen, K. “Immersed Boundary Method for The Simulation of 2D Viscous Flow based on Vorticity–velocity Formulations”, J. Comput. Phys., Vol. 228, pp. 1504–1520, 2009.##
12. Sabetghadam, F. and Shajari Ghasemkheili, A. “Using The Method of Inverse Problems in Implementing the Solid Immersed Boundaries on Vorticity-Streamfunction Formulation of the Incompressible Viscous Fluid Flow”, Modarres Mech. Eng., Vol. 17, No. 10, pp. 397-404, 2017 (in Persian).##
13. Badri, M. A. and Sabetghadam, F. “Implementation of Rigid Solid Boundaries to the Vorticity-Stream Function Formulation of Incompressible Navier-Stokes Equations by Time Dilation”, Modarres Mech. Eng., Vol. 19, no. 5, pp.1241-1252, 2019 (in Persian).##
14. Jause-Labert, C., Godeferd, F. S., and Favier, B. “Numerical Validation of The Volume Penalization Method in Three-dimensional Pseudo-spectral Simulation”, J. Comput. Fluid., Vol. 67, pp. 41-56, 2012.##
15. Intel, Math Kernel Library (MKL), http://www.intel.com/software /products/mkl/

CUDA FFT library, https://www.developer.nvidia.com/cuFFT.##

1. Weinane, E. and Jian-Guol, L. “Vorticity Boundary Condition and Related Issues for Finite Difference Schemes”, J. Comput. Phys., Vol. 124, pp. 368–382, 1996.##
2. Van Der Houwen, P. J., Sommeijer, B. P., and Van Mourik, P. A. “Note on Explicit Parallel Multistep Runge-Kutta Methods”, J.Comput. Appl. Math., Vol. 27, pp. 411-420, 1989.##
3. Peskin C. S. “The Immersed Boundary Method”, Acta Numer., Vol. 11, pp. 479-518, 2002.##
4. Sjögreen, B. and Petersson, N. A. “A Cartesian Embedded Boundary Method for Hyperbolic Conservation laws”, Commu. Comp. Phys., Vol. 2, pp. 1199-1219, 2007.##
5. Sabetghadam, F., Sharafatmandjoor, S., and Norouzi, F. “Fourier Spectral Embedded Boundary Solution of the Poisson’s and Laplace Equations with Dirichlet Boundary Conditions”, J. Comput. Phys., Vol. 228, pp. 55-74, 2009.##
6. Lee, L. and Leveque, R. J. “An Immersed Interface Method for The Incompressible Navier-Stocks Equations, SIAM”, J. of Scientif. Comput., Vol. 25, p. 832, 2003.##
7. Liang, A., Jing, X., and Sun, X., “Constructing Spectral Schemes of The Immersed Interface Method via a Global Description of Discontinuous Functions”, J. Comput. Phys., Vol. 227, no.18, pp. 8341–8366, 2008.##
8. Boyd, J. P. “A Comparison of Numerical Algorithms for Fourier Extension of The First, Second, and Third Kinds”, J. Comput. Phys., Vol. 178, pp. 118-160, 2002.##
9. Gottlieb, D. and Orszag, S. A. “Numerical Analysis of Spectral Methods: Theory and Applications”, Society for Industrial and Applied Mathematics, P. 35, 1977.##
10. Tadmor, E. “Filters, Mollifiers and The Computation of The Gibbs Phenomenon”, Acta Numerica, Vol. 16, pp. 305–378, 2007.##
11. Fang, J., Diebold, M., Higgins, C., and Parlange, M. B. “Towards Oscillation-free Implementation of The Immersed Boundary Method With Spectral-like Methods”, J. Comput. Phys., Vol. 230, p. 8179, 2011.##
12. Wang, Q., Moin, P., and Iaccarino, G. “A High Order Multivariate Approximation Scheme for Scattered Data Sets”, J. Comput. Phys., Vol. 229, No.18, pp. 6343-6361, 2010.##
13. Renka, R. J. and Brown, R. “Algorithm 792: Accuracy Tests of ACM Algorithms for Interpolation of Scattered Data in the Plane” ACM Transactions on Mathematical Software, 25 (1999), pp. 78-94.##
14. Sabetghadam, F., Soltani, E.. and Ghasemi, H. “A Fast Immersed Boundary Fourier Pseudo-Spectral Method for Simulation of the Incompressible Flows”, Int. J. Eng. Educ., Vol. 27, pp. 1457-1466, 2014.##
15. Shepard, “A Two-Dimensional Interpolation Function for Irregularly-Spaced data”, 23^rd Int. Conf. ACM National (ACM '68), P. 517–524, 1968.##
16. Quartapelle, L. “Numerical Solution of The Incompressible Navier–Stokes Equations”, Birkhauer-Verlag, Basel, 1993.##
17. Rempfer, D. “On Boundary Conditions for Incompressible Navier-Stokes Problems”, Appl. Mech. Rev., Vol. 59, p.107, 2006.##
18. Sabetghadam, F., Badri, M.,  Sharafatmandjoor, S., and Kor, H. “Pseduspectral Solution of 2D Incompressible Flow in Moving Immersed Boundary”, 10th Iranian Aerospace Committee Conference, Iran, Tehran, 2011(in Persian).##
19. Sabetghadam, F. and Soltani, E. “Simulation of Solid Body Motion in a Newtonian Fluid Using a Vorticity-based Pseudo-spectral Immersed Boundary Method Augmented by The Radial Basis Functions”, Int. J. Mod. Phys., Vol. 26, p. 1550, 2015.##
20. Quartplle, L. “Vorticity Conditioning in The Computation of Two-dimensional Viscous Flow”, J. Comput. Phys., Vol. 40, pp. 453-477, 1981.##
21. Chinchapatnam, P. P., Djidjeli, K., and Nair, P. B. “Radial Basis Function Meshless Method for The Steady Incompressible Navier-Stokes Equations”, Int. J. Comput. Math., Vol. 84, pp. 1509-1526, 2007.##
22. Larsson, E. and Fornberg, B. “A Numerical Study of Some Radial Basis Function Based Solution Methods for Elliptic PDEs”, Computers and Mathematics with Applications, Vol. 46, pp. 891-902, 2003.##
23. Franke, R. and Nielson, G. “Smooth Interpolation of Large Sets of Scattered Data”, Int. J. Numer. Meth. Eng., Vol. 15, pp. 1691-1704, 1980.##
24. Thacker, W. I., Zhang, J., Watson, L. T., Birch, J. B., Iyer, M. A., and Berry, M. W. “Algorithm 905: SHEPPACK: Modified Shepard Algorithm for Interpolation of Scattered Multivariate Data”, ACM Transactions on Mathematical Software, (TOMS) Vol.37, no. 3, pp. 1-20.##
25. Balaras, E. “Modeling Immersed Boundaries Using an External Force Field on Fixed Cartesian Grids in Large-eddy Simulations”, Computers and Fluids, Vol. 33, pp. 375-404, 2004.##
26. Sugiyama, K., Ii, S., Takeuchi, S., Takagi, S., and Matsumoto, Y. “A Full Eulerian Finite Difference Approach for Solving Fluid-structure Coupling Problems”, J. Comput. Phys.,, Vol. 230, pp. 596–627, 2011.##
27. Fadlun, E. A., Verzicco, R., Orlandi, P., and Mohd-Yusof, J. “Combined Immersed Boundary Finite-difference Methods for Three-dimensional Complex Flow Simulations”, J. Comput. Phys., Vol. 161, p. 35, 2000.##
28. Wu, J. Z., Lu, X. Y., and Zhuang, L. X. “Integral Force Acting on a Body Due to Local Flow Structures”, J. Fluid Mech., Vol. 576, p. 265, 2007.##
29. Noca, F., Shiels, D., and Jeon, D. “A Comparison of Methods for Evaluating Time Dependent Flow Dynamic Forces on Bodies, Using Only Velocity Fields and Their Derivations, J. Fluid. Struct.”, Vol. 13, p. 551, 1999.##
30. Wu, J. Z. H., Pan, Z. L., and Lu, X.Y. “Unsteady Fluid Dynamic Force Solely in Terms of Control-surface Integral”, Physics fluids, Vol. 17, p. 98, 2005.##
31. Wu, J. Z., Lu, X. L. , Yang, Y., and Zhang, R. “Vorticity Dynamics in Complex of Diagnosis and Management”, (P.Y. Chou Memorial Lecture at 13th Asian Congress Fluid Mechanics Dhaka, Bangladesh, Dec. 2010, P. 17.).##
32. Seo, J. H., and Mittal, R. “A Sharp-interface Immersed Boundary Method With Improved Mass Conservation and Reduced Spurious Pressure Oscillations”, J. Comput. Phys., Vol. 230, p. 7347, 2011.##
33. Mohebbian, A. and Rival, D.E. “Assessment of The Derivative-moment Transformation Method for Unsteady-load Estimation”, Experimental Fluids, Vol. 53, p. 319, 2012.##
34. Linnick, M. and Fasel, H. “A High Order Interface Method for Simulating Unsteady Incompressible Flows on Irregular Domains”, J. Comput. Phys,, Vol. 204, pp. 157-192, 2005.##

1. Liu, C., Zheng., X., and Sungz, C. H. “Preconditioned multigrid methods for unsteady incompressible flows”, J. Comput. Phys.,, Vol. 139, P. 139, 1998##
2. Sabetghadam, F., Eskandari, A., Azami, A., and Jalinous, S. “A Stabilized Explicit Direct-forcing Immersed-boundary Method for the Simulation of Incompressible Newtonian Fluid Flow Around Deformable Moving Bodies”, Int. J. Mod. Phys., Vol. 18, p. 46, 2016.##
3. Horowitz, M. and Williamson, C. H. K. “Vortex-induced vibration of a rising and falling cylinder”, J. Fluid Mech., Vol. 658, pp. 1-32, 2010.##
4. Namkoong, K., Yoo, J. Y., and Choi, H. G. “Numerical Analysis of Two-dimensional Motion of a Freely Falling Circular Cylinder in an Infinite Fluid”, J. Fluid Mech., Vol. 604, pp. 33-53, 2008.##
5. Koumoutsakos, P. and Leonard, A. “High-resolution Simulations of The Flow Around an Impulsively Started Cylinder Using Vortex Methods”, J. Fluid Mech., Vol. 296, p. 1, 1995.##
6. Liao, C., Chang, Y., Lin, C., and Mc Donough, J. M. “Simulating Flows With Moving Rigid Boundary Using Immersed-boundary Method”, J. of Computational Fluids, Vol. 39, P. 152, 2010.
7. Luo, H., Dai., H., Ferreira de Sousa P., and Yin, B. “On Numerical Oscillation of the Direct-Forcing Immersed-boundary Method for Moving Boundaries”, J. of Computers and Fluids, Vol. 56, PP. 61-76, 2012.##
8. Ghaari, S. A., Schneider, K., Viazzo, S., and Bontoux, V. “An Efficient Algorithm for Simulation of Forced Deformable Bodies Interacting With Incompressible Flows; Application to Fish Swimming”, 11th World Congress on Computational Mechanics, pp. 787-798, Barcelona, Spain, 2014.##