메뉴 건너뛰기




Volumn 7, Issue 1, 2010, Pages 138-170

Balanced monitoring of flow phenomena in moving mesh methods

Author keywords

Balanced monitor function; Conservative interpolation; Directional adaptation; Hydrodynamics; Implosion problem; Moving mesh method

Indexed keywords


EID: 72449153518     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.2009.09.033     Document Type: Article
Times cited : (36)

References (45)
  • 1
    • 4544370138 scopus 로고    scopus 로고
    • An arbitrary Lagrangian-Eulerian method with adaptive mesh refinement for the solution of the Euler equations
    • Sep
    • R. W. Anderson, N. S. Elliott, and R. B. Pember. An arbitrary Lagrangian-Eulerian method with adaptive mesh refinement for the solution of the Euler equations. J. Comput. Phys., 199:598-617, Sep 2004.
    • (2004) J. Comput. Phys , vol.199 , pp. 598-617
    • Anderson, R.W.1    Elliott, N.S.2    Pember, R.B.3
  • 2
    • 33845638600 scopus 로고    scopus 로고
    • Second-order Godunov-type scheme for reactive flow calculations on moving meshes
    • B. N. Azarenok and T. Tang. Second-order Godunov-type scheme for reactive flow calculations on moving meshes. J. Comput. Phys., 206(1):48-80, 2005.
    • (2005) J. Comput. Phys , vol.206 , Issue.1 , pp. 48-80
    • Azarenok, B.N.1    Tang, T.2
  • 3
    • 0034300742 scopus 로고    scopus 로고
    • Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem
    • October
    • G. Beckett and J. A. Mackenzie. Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem. Appl. Numer. Math., 35:87-109, October 2000.
    • (2000) Appl. Numer. Math , vol.35 , pp. 87-109
    • Beckett, G.1    Mackenzie, J.A.2
  • 4
    • 35748953595 scopus 로고    scopus 로고
    • Analysis of slope limiters on irregular grids
    • Technical Report 2005-0490, AIAA Paper, May 2005. Reno, NV, Jan
    • M. J. Berger,M. J. Aftosmis, and S.M.Murman. Analysis of slope limiters on irregular grids. Technical Report 2005-0490, AIAA Paper, May 2005. Reno, NV, Jan. 2005.
    • (2005)
    • Berger, M.J.1    Aftosmis, M.J.2    Murman, S.M.3
  • 5
    • 0002255324 scopus 로고
    • An adaptive grid with directional control
    • J. U. Brackbill. An adaptive grid with directional control. J. Comput. Phys., 108(1):38-50, 1993.
    • (1993) J. Comput. Phys , vol.108 , Issue.1 , pp. 38-50
    • Brackbill, J.U.1
  • 6
    • 49049134162 scopus 로고    scopus 로고
    • J. U. Brackbill and J. S. Saltzman. Adaptive zoning for singular problems in two dimensions. J. Comput. Phys., 46:342-368, 1982.
    • J. U. Brackbill and J. S. Saltzman. Adaptive zoning for singular problems in two dimensions. J. Comput. Phys., 46:342-368, 1982.
  • 7
    • 0033294022 scopus 로고    scopus 로고
    • A study of monitor functions for two-dimensional adaptive mesh generation. SIAMJ
    • W.-M. Cao, W.-Z. Huang, and R. D. Russell. A study of monitor functions for two-dimensional adaptive mesh generation. SIAMJ. Sci. Comput., 20(6):1978-1994, 1999.
    • (1999) Sci. Comput , vol.20 , Issue.6 , pp. 1978-1994
    • Cao, W.-M.1    Huang, W.-Z.2    Russell, R.D.3
  • 8
    • 0035922234 scopus 로고    scopus 로고
    • An efficient dynamically adaptive mesh for potentially singular solutions
    • H. D. Ceniceros and T. Y. Hou. An efficient dynamically adaptive mesh for potentially singular solutions. J. Comput. Phys., 172(2):609-639, 2001.
    • (2001) J. Comput. Phys , vol.172 , Issue.2 , pp. 609-639
    • Ceniceros, H.D.1    Hou, T.Y.2
  • 9
    • 0040754068 scopus 로고    scopus 로고
    • On the invertibility of mappings arising in 2D grid generation problems
    • P. Clément, R. Hagmeijer, and G. Sweers. On the invertibility of mappings arising in 2D grid generation problems. Numerische Mathematik, 73(1):37-51, 1996.
    • (1996) Numerische Mathematik , vol.73 , Issue.1 , pp. 37-51
    • Clément, P.1    Hagmeijer, R.2    Sweers, G.3
  • 10
    • 85150404154 scopus 로고    scopus 로고
    • Y.-N. Di, R. Li, and T. Tang. A generalmoving mesh framework in 3D and its application for simulating the mixture of multi-phase flows. Commun. Comput. Phys., 3(3):582-602, 2008.
    • Y.-N. Di, R. Li, and T. Tang. A generalmoving mesh framework in 3D and its application for simulating the mixture of multi-phase flows. Commun. Comput. Phys., 3(3):582-602, 2008.
  • 11
    • 19744364449 scopus 로고    scopus 로고
    • Moving mesh finite element methods for the incompressible Navier-Stokes equations. SIAMJ
    • Y.-N. Di, R. Li, T. Tang, and P.-W. Zhang. Moving mesh finite element methods for the incompressible Navier-Stokes equations. SIAMJ. Sci. Comput., 26(3):1036-1056, 2005.
    • (2005) Sci. Comput , vol.26 , Issue.3 , pp. 1036-1056
    • Di, Y.-N.1    Li, R.2    Tang, T.3    Zhang, P.-W.4
  • 13
    • 33845602193 scopus 로고    scopus 로고
    • An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics
    • Jan
    • J.-Q. Han and H. Z. Tang. An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics. J. Comput. Phys., 220:791-812, Jan 2007.
    • (2007) J. Comput. Phys , vol.220 , pp. 791-812
    • Han, J.-Q.1    Tang, H.Z.2
  • 14
    • 0000876320 scopus 로고
    • On upstreamdifferencing and Godunov-type schemes for hyperbolic conservation laws
    • A.Harten, P. D. Lax, and B. Van Leer. On upstreamdifferencing and Godunov-type schemes for hyperbolic conservation laws. SIAMReview, 25(1):35-61, 1983.
    • (1983) SIAMReview , vol.25 , Issue.1 , pp. 35-61
    • Harten, A.1    Lax, P.D.2    Van Leer, B.3
  • 15
    • 0037466062 scopus 로고    scopus 로고
    • The wall-jetting effect in Mach refiection: Theoretical consideration and numerical investigation
    • L. F. Henderson, E. I. Vasilev, G. Ben-Dor, and T. Elperin. The wall-jetting effect in Mach refiection: theoretical consideration and numerical investigation. J. Fluid Mech., 479:259-286, 2003.
    • (2003) J. Fluid Mech , vol.479 , pp. 259-286
    • Henderson, L.F.1    Vasilev, E.I.2    Ben-Dor, G.3    Elperin, T.4
  • 16
    • 33751100721 scopus 로고    scopus 로고
    • Mathematical principles of anisotropic mesh adaptation
    • W.-Z. Huang. Mathematical principles of anisotropic mesh adaptation. Commun. Comput. Phys., 1:276-310, 2006.
    • (2006) Commun. Comput. Phys , vol.1 , pp. 276-310
    • Huang, W.-Z.1
  • 17
    • 0000311286 scopus 로고    scopus 로고
    • Practical aspects of formulation and solution of moving mesh partial differential equations
    • W.-Z. Huang. Practical aspects of formulation and solution of moving mesh partial differential equations. J. Comput. Phys., 171(2):753-775, 2001.
    • (2001) J. Comput. Phys , vol.171 , Issue.2 , pp. 753-775
    • Huang, W.-Z.1
  • 18
    • 0001917909 scopus 로고    scopus 로고
    • Multidimensional slope limiters forMUSCL-type finite volume schemes on unstructured grids
    • October
    • M. E. Hubbard. Multidimensional slope limiters forMUSCL-type finite volume schemes on unstructured grids. J. Comput. Phys., 155(1):54-74,October 1999.
    • (1999) J. Comput. Phys , vol.155 , Issue.1 , pp. 54-74
    • Hubbard, M.E.1
  • 19
    • 0001741885 scopus 로고    scopus 로고
    • Aunified coordinate systemfor solving the two-dimensional Euler equations
    • Aug
    • W.H.Hui, P. Y. Li, and Z.W. Li. Aunified coordinate systemfor solving the two-dimensional Euler equations. J. Comput. Phys., 153:596-637,Aug 1999.
    • (1999) J. Comput. Phys , vol.153 , pp. 596-637
    • Hui, W.H.1    Li, P.Y.2    Li, Z.W.3
  • 20
    • 0038517141 scopus 로고    scopus 로고
    • A two-dimensional moving finite element method with local refinement based on a posteriori error estimates
    • J. Lang, W.-M. Cao, W.-Z. Huang, and R. D. Russell. A two-dimensional moving finite element method with local refinement based on a posteriori error estimates. Appl. Numer. Math., 46(1):75-94, 2003.
    • (2003) Appl. Numer. Math , vol.46 , Issue.1 , pp. 75-94
    • Lang, J.1    Cao, W.-M.2    Huang, W.-Z.3    Russell, R.D.4
  • 21
    • 0001528721 scopus 로고    scopus 로고
    • Solution of two-dimensional Riemann problems of gas dynamics by positive schemes. SIAMJ
    • P. D. Lax and X.-D. Liu. Solution of two-dimensional Riemann problems of gas dynamics by positive schemes. SIAMJ. Sci. Comput., 19(2):319-340, 1998.
    • (1998) Sci. Comput , vol.19 , Issue.2 , pp. 319-340
    • Lax, P.D.1    Liu, X.-D.2
  • 22
    • 1942511452 scopus 로고    scopus 로고
    • Comparison of several difference schemes on 1D and 2D test problems for the Euler equations. SIAMJ
    • R. Liska and B. Wendroff. Comparison of several difference schemes on 1D and 2D test problems for the Euler equations. SIAMJ. Sci. Comput., 25(3):995-1017, 2003.
    • (2003) Sci. Comput , vol.25 , Issue.3 , pp. 995-1017
    • Liska, R.1    Wendroff, B.2
  • 23
    • 0038090587 scopus 로고    scopus 로고
    • AMRVAC: A multidimensional grid-adaptive magneto fluid dynamics code
    • M. Nool and R. Keppens. AMRVAC: a multidimensional grid-adaptive magneto fluid dynamics code. Comp. Meth. Appl. Math., 2:92-109, 2002.
    • (2002) Comp. Meth. Appl. Math , vol.2 , pp. 92-109
    • Nool, M.1    Keppens, R.2
  • 24
    • 0001328401 scopus 로고
    • Calculation of intersection of non-steady shock waves with obstacles
    • V. V. Rusanov. Calculation of intersection of non-steady shock waves with obstacles. J. Comput. Math. Phys. USSR, 1:267-279, 1961.
    • (1961) J. Comput. Math. Phys. USSR , vol.1 , pp. 267-279
    • Rusanov, V.V.1
  • 25
    • 0003332686 scopus 로고
    • Numerical solution of the Riemann problem for two-dimensional gas dynamics. SIAMJ
    • C. W. Schulz-Rinne, J. P. Collins, and H. M. Glaz. Numerical solution of the Riemann problem for two-dimensional gas dynamics. SIAMJ. Sci. Comput., 14(6):1394-1414, 1993.
    • (1993) Sci. Comput , vol.14 , Issue.6 , pp. 1394-1414
    • Schulz-Rinne, C.W.1    Collins, J.P.2    Glaz, H.M.3
  • 27
    • 33846394104 scopus 로고    scopus 로고
    • Adaptive moving mesh methods for two-dimensional resistive magneto-hydrodynamic PDE models
    • May
    • Z.-J. Tan. Adaptive moving mesh methods for two-dimensional resistive magneto-hydrodynamic PDE models. Comput. Fluids, 36:758-771,May 2007.
    • (2007) Comput. Fluids , vol.36 , pp. 758-771
    • Tan, Z.-J.1
  • 28
    • 4544281285 scopus 로고    scopus 로고
    • Movingmeshmethodswith locally varying time steps
    • October
    • Z.-J. Tan, Z.-R. Zhang, Y.-Q.Huang, and T. Tang. Movingmeshmethodswith locally varying time steps. J. Comput. Phys., 200:347-367,October 2004.
    • (2004) J. Comput. Phys , vol.200 , pp. 347-367
    • Tan, Z.-J.1    Zhang, Z.-R.2    Huang, Y.Q.3    Tang, T.4
  • 29
    • 0038346370 scopus 로고    scopus 로고
    • An adaptivemesh redistributionmethod for nonlinear Hamilton-Jacobi equations in two- and three-dimensions
    • H. Z. Tang, T. Tang, and P.-W. Zhang. An adaptivemesh redistributionmethod for nonlinear Hamilton-Jacobi equations in two- and three-dimensions. J. Comput. Phys., 188(2):543-572, 2003.
    • (2003) J. Comput. Phys , vol.188 , Issue.2 , pp. 543-572
    • Tang, H.Z.1    Tang, T.2    Zhang, P.-W.3
  • 30
    • 0038704068 scopus 로고    scopus 로고
    • Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws. SIAMJ
    • H. Z. Tang and T. Tang. Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws. SIAMJ. Numer. Anal., 41(2):487-515, 2003.
    • (2003) Numer. Anal , vol.41 , Issue.2 , pp. 487-515
    • Tang, H.Z.1    Tang, T.2
  • 31
    • 33846343613 scopus 로고    scopus 로고
    • A moving mesh method for the Euler flow calculations using a directional monitor function
    • H. Z. Tang. A moving mesh method for the Euler flow calculations using a directional monitor function. Commun. Comput. Phys., 1:656-676, 2006.
    • (2006) Commun. Comput. Phys , vol.1 , pp. 656-676
    • Tang, H.Z.1
  • 32
    • 33646916947 scopus 로고    scopus 로고
    • Moving mesh methods for computational fluid dynamics
    • Z.-C. Shi, Z. Chen, T. Tang, and D. Yu, editors, Recent Advances in Adaptive Computation, of, American Mathematical Society
    • T. Tang. Moving mesh methods for computational fluid dynamics. In Z.-C. Shi, Z. Chen, T. Tang, and D. Yu, editors, Recent Advances in Adaptive Computation, volume 383 of Contemporary Mathematics, pp. 185-218. American Mathematical Society, 2005.
    • (2005) Contemporary Mathematics , vol.383 , pp. 185-218
    • Tang, T.1
  • 33
    • 0003122153 scopus 로고    scopus 로고
    • E. F. Toro,M. Spruce, andW. Speares. Restoration of the contact surface in theHLL-Riemann solver. Shock Waves, 4(1):25-34, 1994.
    • E. F. Toro,M. Spruce, andW. Speares. Restoration of the contact surface in theHLL-Riemann solver. Shock Waves, 4(1):25-34, 1994.
  • 36
    • 34548390526 scopus 로고    scopus 로고
    • Hybrid block-AMR in cartesian and curvilinear coordinates: MHD applications
    • September
    • B. van der Holst and R. Keppens. Hybrid block-AMR in cartesian and curvilinear coordinates: MHD applications. J. Comput. Phys., 226(1):925-946, September 2007.
    • (2007) J. Comput. Phys , vol.226 , Issue.1 , pp. 925-946
    • van der Holst, B.1    Keppens, R.2
  • 37
    • 3142757150 scopus 로고
    • Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow
    • March
    • B. van Leer. Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow. J. Comput. Phys., 23:263-275, March 1977.
    • (1977) J. Comput. Phys , vol.23 , pp. 263-275
    • van Leer, B.1
  • 38
    • 49449129017 scopus 로고
    • Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection
    • March
    • B. van Leer. Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection. J. Comput. Phys., 23:276-299,March 1977.
    • (1977) J. Comput. Phys , vol.23 , pp. 276-299
    • van Leer, B.1
  • 39
    • 33646935170 scopus 로고    scopus 로고
    • A robust moving mesh finite volume method applied to 1D hyperbolic conservation laws from magnetohydrodynamics
    • A. van Dam and P. A. Zegeling. A robust moving mesh finite volume method applied to 1D hyperbolic conservation laws from magnetohydrodynamics. J. Comput. Phys., 216:526-546, 2006.
    • (2006) J. Comput. Phys , vol.216 , pp. 526-546
    • van Dam, A.1    Zegeling, P.A.2
  • 40
    • 0012592932 scopus 로고
    • Adaptive-mesh zoning by the equipotential method
    • Technical Report UCID-19062, Lawrence Livermore Laboratory
    • A. M. Winslow. Adaptive-mesh zoning by the equipotential method. Technical Report UCID-19062, Lawrence Livermore Laboratory, 1981.
    • (1981)
    • Winslow, A.M.1
  • 41
    • 48749139407 scopus 로고
    • The numerical simulation of two-dimensional fluid flow with strong shocks
    • April
    • P. Woodward and P. Colella. The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys., 54:115-173, April 1984.
    • (1984) J. Comput. Phys , vol.54 , pp. 115-173
    • Woodward, P.1    Colella, P.2
  • 42
    • 23944462472 scopus 로고    scopus 로고
    • On resistive MHD models with adaptive moving meshes
    • P. A. Zegeling. On resistive MHD models with adaptive moving meshes. J. Sci. Comput., 24(2):263-284, 2005.
    • (2005) J. Sci. Comput , vol.24 , Issue.2 , pp. 263-284
    • Zegeling, P.A.1
  • 43
    • 76449109506 scopus 로고    scopus 로고
    • Theory and application of adaptive moving grid methods
    • T. Tang and J. Xu, editors, chapter 7, pp, Science Press, Beijing
    • P. A. Zegeling. Theory and application of adaptive moving grid methods. In T. Tang and J. Xu, editors, Adaptive Computations: Theory and Algorithms, chapter 7, pp. 251-296. Science Press, Beijing, 2007.
    • (2007) Adaptive Computations: Theory and Algorithms , pp. 251-296
    • Zegeling, P.A.1
  • 44
    • 33646898234 scopus 로고    scopus 로고
    • Robust and efficient adaptive moving mesh solution of the 2-D Euler equations
    • Z.-C. Shi, Z. Chen, T. Tang, and D. Yu, editors, Recent Advances in Adaptive Computation, of, American Mathematical Society
    • P. A. Zegeling, W. D. de Boer, and H. Z. Tang. Robust and efficient adaptive moving mesh solution of the 2-D Euler equations. In Z.-C. Shi, Z. Chen, T. Tang, and D. Yu, editors, Recent Advances in Adaptive Computation, volume 383 of Contemporary Mathematics, pp. 419-430. American Mathematical Society, 2005.
    • (2005) Contemporary Mathematics , vol.383 , pp. 419-430
    • Zegeling, P.A.1    de Boer, W.D.2    Tang, H.Z.3
  • 45
    • 76449113313 scopus 로고    scopus 로고
    • Z. Zhang. Moving mesh method with conservative interpolation based on L2-projection. Commun. Comput. Phys., 1:930-944, 2006.
    • Z. Zhang. Moving mesh method with conservative interpolation based on L2-projection. Commun. Comput. Phys., 1:930-944, 2006.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.