A moving-mesh gradient smoothing method for compressible CFD problems

Mathematical Models and Methods in Applied Sciences

Volumn 23, Issue 2, 2013, Pages 273-305

  Yao, Jianyao ^a   Liu, G R ^a   Qian, Dong ^a   Chen, Chung Lung ^b   Xu, George X ^c  

^a 705 Engineering Research Center   (United States)

^b University of Missouri   (United States)

^c The Concourse   (Singapore)

Author keywords

CFD; Gradient smoothing method (GSM); Method of manufactured solutions (MMS); Moving mesh; Verification

Indexed keywords

3 LEVELS; CELL EDGES; COMPRESSIBLE NAVIER-STOKES EQUATIONS; DIFFERENCING SCHEME; DIFFERENT TIME STEPS; FIELD VARIABLES; FLUX DIFFERENCE SPLITTING; GRADIENT SMOOTHING; GRADIENT SMOOTHING METHODS; METHOD OF MANUFACTURED SOLUTIONS (MMS); MOVING MESH; ORDER OF ACCURACY; SECOND ORDERS; SECOND-ORDER ACCURACY; SECOND-ORDER SCHEME; SPATIAL DERIVATIVES; SPATIAL DISCRETIZATIONS; TEMPORAL DISCRETIZATION; TRIANGLE MESH; UNSTRUCTURED MESHES;

COMPUTATIONAL MECHANICS; NAVIER STOKES EQUATIONS; VERIFICATION;

COMPUTATIONAL FLUID DYNAMICS;

EID: 84872424480     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202513400046     Document Type: Article

References (71)

1. G. R. Liu, Mesh Free Methods: Moving Beyond the Finite Element method, 2nd edn. (CRC Press, 2009).
2. G. R. Liu and G. X. Xu, A gradient smoothing method (GSM) for fluid dynamics problems, Int. J. Numer. Methods Fluids 58 (2008) 1101-1133.
3. T. Tezduyar, S. Aliabadi, M. Behr, A. Johnson, V. Kalro and M. Litke, Flow simulation and high performance computing, Comput. Mech. 18 (1996) 397-412. (Pubitemid 126545878)
4. T. E. Tezduyar, CFD methods for three-dimensional computation of complex flow problems, J. Wind Engrg. Indus. Aerodynam. 81 (1999) 97-116. (Pubitemid 29421370)
5. T. E. Tezduyar, Finite element methods for flow problems with moving boundaries and interfaces, Arch. Comput. Methods Engrg. 8 (2001) 83-130. (Pubitemid 33679846)
6. K. Takizawa and T. E. Tezduyar, Computational methods for parachute fluidstructure interactions, Arch. Comput. Methods Engrg. 19 (2012) 125-169.
7. K. Takizawa, Y. Bazilevs and T. E. Tezduyar, Space-time and ALE-VMS techniques for patient-specific cardiovascular fluid-structure interaction modeling, Arch. Comput. Methods Engrg. 19 (2012) 171-225.
8. K. Takizawa and T. E. Tezduyar, Space-time fluid-structure interaction methods, Math. Models Methods Appl. Sci. 22 (2012) 1230001.
9. Y. Bazilevs, M.-C. Hsu, K. Takizawa and T. E. Tezduyar, ALE-VMS and STVMS methods for computer modeling of wind-turbine rotor aerodynamics and fluidstructure interaction, Math. Models Methods Appl. Sci. 22 (2012) 1230002.
10. T. J. R. Hughes and T. E. Tezduyar, Finite element methods for first-order hyperbolic systems with particular emphasis on compressible Euler equations, Computer Methods Appl. Mech. Engrg. 45 (1984) 217-284. (Pubitemid 14640721)
11. G. J. Le Beau, S. E. Ray, S. K. Aliabadi and T. E. Tezduyar, SUPG finite element computation of compressible flows with the entropy and conservation variables formulations, Computer Methods Appl. Mech. Engrg. 104 (1993) 397-422.
12. T. E. Tezduyar, M. Senga and D. Vicker, Computation of inviscid supersonic flows around cylinders and spheres with SUPG formulation and YZβ shock-capturing, Comput. Mech. 38 (2006) 469-481. (Pubitemid 43967454)
13. G. X. Xu, G. R. Liu and A. Tani, An adaptive gradient smoothing method for fluid dynamics problems, Int. J. Numer. Methods Fluids 62 (2010) 499-529.
14. G. X. Xu, E. Li, V. Tan and G. R. Liu, Simulation of steady and unsteady incompressible flow using gradient smoothing method (GSM), Computers Struct. 90-91 (2012) 131-144.
15. E. Li, V. Tan, G. X. Xu, G. R. Liu and Z. C. He, A novel linearly-weighted gradient smoothing method (LWGSM) in the simulation of fluid dynamics problem, Computers Fluids 50 (2011) 104-119.
16. E. Li, G. R. Liu, G. X. Xu, V. Tan and Z. C. He, Numerical modeling and simulation of pulsatile blood flow in rigid vessel using gradient smoothing method, Engrg. Anal. Boundary Elements 36 (2012) 322-334.
17. C. S. Peskin, The immersed boundary method, Acta Numer. 11 (2002) 479-517.
18. R. Mittal and G. Iaccarino, Immersed boundary methods, Ann. Rev. Fluid Dynam. 37 (2005) 239-261. (Pubitemid 40301258)
19. L. Zhang, A. Gerstenberger, X.Wang andW. K. Liu, Immersed finite element method, Computer Methods Appl. Mech. Engrg. 193 (2004) 2051-2067. (Pubitemid 38463397)
20. C. W. Hirt, A. A. Amsden and J. J. Cook, An arbitrary Lagrangian-Eulerian computing method for all flow speed, J. Comput. Phys. 14 (1974) 227-253.
21. J. Donea, S. Giuliani and J. P. Halleux, An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions, Computer Methods Appl. Mech. Engrg. 33 (1982) 689-723.
22. J. T. Batina, Unsteady Euler airfoil solutions using unstructured dynamic meshes, AIAA paper (1989) 89-0115.
23. B. Koobus and C. Farhat, Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes, Computer Methods Appl. Mech. Engrg. 170 (1999) 103-129.
24. T. E. Tezduyar, Stabilized finite element formulations for incompressible flow computations. Adv. Appl. Mech. 28 (1992) 1-44.
25. T. E. Tezduyar and S. Sathe, Modeling of fluid-structure interactions with the space- time finite elements: Solution techniques, Int. J. Numer. Methods Fluids 54 (2007) 855-900. (Pubitemid 47009683)
26. K. Takizawa and T. E. Tezduyar, Multiscale space-time fluid-structure interaction techniques, Comput. Mech. 48 (2011) 247-267.
27. T. E. Tezduyar, S. Aliabadi, M. Behr, A. Johnson and S. Mittal, Parallel finite element computation of 3D flows, Computer 26 (1993) 27-36.
28. A. A. Johnson and T. E. Tezduyar, Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces, Computer Methods Appl. Mech. Engrg. 119 (1994) 73-94. (Pubitemid 289971)
29. K. Stein, T. E. Tezduyar and R. Benney, Mesh moving techniques for fluid-structure interactions with large displacements, J. Appl. Mech. 70 (2003) 58-63.
30. K. Stein, T. E. Tezduyar and R. Benney, Automatic mesh update with the solidextension mesh moving technique, Computer Methods Appl. Mech. Engrg. 193 (2004) 2019-2032. (Pubitemid 38463395)
31. A. A. Johnson and T. E. Tezduyar, Advanced mesh generation and update methods for 3d flow simulations, Comput. Mech. 23 (1999) 130-143.
32. K. Takizawa, T. Spielman and T. E. Tezduyar, Space-time FSI modeling and dynamical analysis of spacecraft parachutes and parachute clusters, Comput. Mech. 48 (2011) 345-364.
33. W. K. Liu et al., Immersed finite element method and its applications to biological systems, Computer Methods Appl. Mech. Engrg. 195 (2006) 1722-1749. (Pubitemid 43116272)
34. J. De Hart et al., A three-dimensional computational analysis of fluid-structure interaction in the aortic valve, J. Biomech. 36 (2003) 103-112. (Pubitemid 35448099)
35. Z. Q. Zhang, J. Yao and G. R. Liu, An immersed smoothed finite element method for fluid-structure interaction problems, Int. J. Comput. Methods 8 (2011) 747-757.
36. Z. Q. Zhang, G. R. Liu and B. C. Khoo, Immersed smoothed finite element method for two-dimensional fluid-structure interaction problems, Int. J. Numer. Methods Engrg. 90 (2012) 1292-1320.
37. Z. Q. Zhang, G. R. Liu and B. C. Khoo, A three-dimensional immersed smoothed finite element method (3D IS-FEM) for fluid-structure interaction problems, Comput. Mech., DOI: 10.1007/s00466-012-0710-1.
38. J. Yao, G. R. Liu, D. A. Narmoneva, R. B. Hinton and Z. Q. Zhang, Immersed smoothed finite element method for fluid structure interaction simulation of aortic valves, Comput. Mech., DOI: 10.1007/s00466-012-0781-z.
39. K. Takizawa, B. Henicke, A. Puntel, T. Spielman and T. E. Tezduyar, Space-time computational techniques for the aerodynamics of flapping wings, J. Appl. Mech. 79 (2012) 010903.
40. V. Kalro and T. E. Tezduyar, A parallel 3D computational method for fluid-structure interactions in parachute systems, Computer Methods Appl. Mech. Engrg. 190 (2010) 321-332.
41. T. E. Tezduyar and Y. Osawa, Fluid-structure interactions of a parachute crossing the far wake of an aircraft. Computer Methods Appl. Mech. Engrg. 191 (2001) 717-726. (Pubitemid 34004498)
42. C. Farhat, K. G. van der Zee and P. Geuzaine, Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity, Computer. Methods Appl. Mech. Engrg. 195 (2006) 1973-2001. (Pubitemid 43193530)
43. R. Kamakoti and W. Shyy, Fluid-structure interaction for aeroelastic applications, Progr. Aerospace Sci. 40 (2004) 535-558. (Pubitemid 40391501)
44. K. Ramakrishnan, D. A. Gottfried, P. B. Lawless and S. Fleeter, Development and application of an arbitrary Lagrangian-Eulerian solver for turbomachinery aeromechanics, J. Propulsion Power 25 (2009) 642-652.
45. J. Hron and S. Turek, A monolithic FEM/multigrid solver for an ALE formulation of fluid-structure interaction with applications in biomechanics, in Lecture Notes in Computational Science and Engineering: Fluid-Structure Interaction 53 (2006) 146-170.
46. P. Moireau et al., External tissue support and fluid-structure simulation in blood flows, Biomech. Model Mechanobiol. 11 (2012) 1-18.
47. T. E. Tezduyar, K. Takizawa, C. Moorman, S. Wright and J. Christopher, Multiscale sequentially-coupled arterial FSI techniques, Comput. Mech. 46 (2010) 17-29.
48. K. Takizawa, C. Moorman, S. Wright, J. Christopher and T. E. Tezduyar, Wall shear stress calculations in space-time finite element computation of arterial fluid-structure interactions, Comput. Mech. 46 (2010) 31-41.
49. R. Torii, M. Oshima, T. Kobayashi, K. Takagi and T. E. Tezduyar, Role of 0D peripheral vasculature model in fluid-structure interaction modeling of aneurysms, Comput. Mech. 46 (2010) 43-52.
50. W. Dettmer and D. Peric, A computational framework for fluid-structure interaction: Finite element formulation and applications, Computer Methods Appl. Mech. Engrg. 195 (2006) 5754-5779. (Pubitemid 43942200)
51. R. van Loon, P. D. Anderson, F. N. van de Vosse and S. J. Sherwin, Comparison of various fluid-structure interaction methods for deformable bodies, Computers Structures 85 (2007) 833-843. (Pubitemid 46719347)
52. K. Takizawa, B. Henicke, T. E. Tezduyar, M.-C. Hsu and Y. Bazilevs, Stabilized space-time computation of wind-turbine rotor aerodynamics, Comput. Mech. 48 (2011) 333-344.
53. K. Takizawa, B. Henicke, D. Montes, T. E. Tezduyar, M.-C. Hsu and Y. Bazilevs, Numerical performance studies for the stabilized space-time computation of windturbine rotor aerodynamics, Comput. Mech. 48 (2011) 647-657.
54. W. L. Oberkampf and T. G. Trucano, Verification and validation in computational fluid dynamics, Progr. Aerospace Sci. 38 (2002) 209-272. (Pubitemid 34863048)
55. W. L. Oberkampf and T. G. Trucano, Verification and validation benchmarks, Nucl. Engrg. Design 238 (2008) 716-743. (Pubitemid 351253682)
56. C. J. Roy, C. C. Nelson, T. M. Smith and C. C. Ober, Verification of Euler/Navier- Stokes codes using the method of manufactured solutions, Int. J. Numer. Methods Fluids 44 (2004) 599-620. (Pubitemid 38211601)
57. L. Eca, M. Hoekstra, A. Hay and D. Pelletier, On the construction of manufactured solutions for one- and two-equation eddy-viscosity models, Int. J. Numer. Methods Fluids 54 (2007) 119-154. (Pubitemid 46672612)
58. S. Etienne, A. Garon and D. Pelletier, Perspective on the geometric conservation law and finite element methods for ALE simulations of incompressible flow, J. Comput. Phys. 228 (2009) 2313-2333.
59. C. J. Roy and A. Raju, Estimation of discretization errors using the method of nearby problems, AIAA J. 45 (2007) 1232-1243. (Pubitemid 46997890)
60. C. J. Roy and A. J. Sinclair, On the generation of exact solutions for evaluating numerical schemes and estimating discretization error, J. Comput. Phys. 228 (2009) 1790-1802.
61. L. Lucy, A numerical approach to testing the fission hypothesis, Astron. J. 82 (1977) 1013-1024.
62. G. R. Liu and M. B. Liu, Smoothing Particle Hydrodynamics - A Meshfree Particle Method (World Scientific, 2003).
63. P. L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys. 43 (1981) 357-382.
64. J. Blazek, Computational Fluid Dynamics: Principles and Applications, 2nd edn. (Elsevier, 2005).
65. V. Venkatakrishnan, Convergence to steady-state solutions of the Euler equations on unstructured grids with limiters, J. Comput. Phys. 118 (1995) 120-130.
66. P. Geuzaine, C. Grandmont and C. Farhat, Design and analysis of ALE schemes with provable second-order time-accuracy for inviscid and viscous flow simulations, J. Comput. Phys. 191 (2003) 206-227. (Pubitemid 37223476)
67. N. Qin, X. Liu and H. Xia, An efficient moving grid algorithm for large deformation, Mod. Phys. Lett. B 19 (2005) 1499-1502. (Pubitemid 43111988)
68. J. A. S. Witteveen, Explicit and robust inverse distance weighting mesh deformation for CFD, AIAA 2010-165 (2010).
69. S. Mittal and T. E. Tezduyar, A finite element study of incompressible flows past oscillating cylinders and airfoils, Int. J. Numer. Methods Fluids 15 (1992) 1073-1118. (Pubitemid 23574530)
70. K. D. Jones, C. M. Dohring and M. F. Platzer, Experimental and computational investigation of the Knoller-Betz effect, AIAA J. 36 (1998) 1240-1246. (Pubitemid 128550504)
71. C. Liang, K. Ou, S. Premasuthan, A. Jameson and Z. J. Wang, High-order accurate simulations of unsteady flow past plunging and pitching airfoils, Computers Fluids 40 (2010) 236-248.