메뉴 건너뛰기




Volumn 50, Issue 4, 2008, Pages 723-752

Logically rectangular grids and finite volume methods for PDEs in circular and spherical domains

Author keywords

Circular domain; Finite volume methods; Grid transformations; Hyperbolic PDEs; Spherical domain

Indexed keywords

CIRCULAR DOMAIN; FINITE VOLUME METHODS; GRID TRANSFORMATIONS; HYPERBOLIC PDES; SPHERICAL DOMAIN;

EID: 56349111880     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/060664094     Document Type: Review
Times cited : (101)

References (49)
  • 1
    • 11844285712 scopus 로고    scopus 로고
    • Implementation of an atmosphere ocean general circulation model on the expanded spherical cube
    • A. ADCROFT, J.-M. CAMPIN, C. HILL, AND J. MARSHALL, Implementation of an atmosphere ocean general circulation model on the expanded spherical cube, Monthly Weather Rev., 132 (2004), pp. 2845-2863.
    • (2004) Monthly Weather Rev , vol.132 , pp. 2845-2863
    • ADCROFT, A.1    CAMPIN, J.-M.2    HILL, C.3    MARSHALL, J.4
  • 2
    • 0031215973 scopus 로고    scopus 로고
    • A Cartesian grid projection method for the incompressible Euler equations in complex geometries
    • A. S. ALMGREN, J. B. BELL, P. COLELLA, AND T. MARTHALER., A Cartesian grid projection method for the incompressible Euler equations in complex geometries, SIAM J. Sci. Comput., 18 (1997), pp. 1289-1309.
    • (1997) SIAM J. Sci. Comput , vol.18 , pp. 1289-1309
    • ALMGREN, A.S.1    BELL, J.B.2    COLELLA, P.3    MARTHALER, T.4
  • 3
    • 0031642221 scopus 로고    scopus 로고
    • Topologically rectangular grids in the parallel simulation of semiconductor devices
    • A. ASENOV, A. R. BROWN, S. ROY, AND J. R. BARKER, Topologically rectangular grids in the parallel simulation of semiconductor devices, VLSI Design, 6 (1998), pp. 91-95.
    • (1998) VLSI Design , vol.6 , pp. 91-95
    • ASENOV, A.1    BROWN, A.R.2    ROY, S.3    BARKER, J.R.4
  • 4
    • 0033038309 scopus 로고    scopus 로고
    • A two-dimensional numerical study of spatial pattern formation in interacting Turing systems
    • R. BARRIO, C. VAREA, J. ARAGÓN, AND P. MAINI, A two-dimensional numerical study of spatial pattern formation in interacting Turing systems, Bull. Math. Biol., 61 (1999), pp. 483-505.
    • (1999) Bull. Math. Biol , vol.61 , pp. 483-505
    • BARRIO, R.1    VAREA, C.2    ARAGÓN, J.3    MAINI, P.4
  • 6
    • 0008352647 scopus 로고
    • Stable boundary conditions for Cartesian grid calculations
    • M. BERGER AND R. J. LEVEQUE, Stable boundary conditions for Cartesian grid calculations, Comput. Systems Engrg., 1 (1990), pp. 305-311.
    • (1990) Comput. Systems Engrg , vol.1 , pp. 305-311
    • BERGER, M.1    LEVEQUE, R.J.2
  • 7
    • 48749141209 scopus 로고
    • Adaptive mesh refinement for hyperbolic partial differential equations
    • M. BERGER AND J. OLIGER, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys., 53 (1984), pp. 484-512.
    • (1984) J. Comput. Phys , vol.53 , pp. 484-512
    • BERGER, M.1    OLIGER, J.2
  • 8
    • 11744289966 scopus 로고
    • Local adaptive mesh refinement for shock hydrodynamics
    • M. J. BERGER AND P. COLELLA, Local adaptive mesh refinement for shock hydrodynamics, J. Comput. Phys., 82 (1989), pp. 64-84.
    • (1989) J. Comput. Phys , vol.82 , pp. 64-84
    • BERGER, M.J.1    COLELLA, P.2
  • 9
    • 3042707695 scopus 로고    scopus 로고
    • k-box methods for the approximation of hyperbolic conservation laws on irregular grids
    • M. J. BERGER, C. HELZEL, AND R. J. LEVEQUE, k-box methods for the approximation of hyperbolic conservation laws on irregular grids, SIAM J. Numer. Anal., 41 (2003), pp. 893-918.
    • (2003) SIAM J. Numer. Anal , vol.41 , pp. 893-918
    • BERGER, M.J.1    HELZEL, C.2    LEVEQUE, R.J.3
  • 10
    • 0001762370 scopus 로고    scopus 로고
    • Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems
    • M. J. BERGER AND R. J. LEVEQUE, Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems, SIAM J. Numer. Anal., 35 (1998), pp. 2298-2316.
    • (1998) SIAM J. Numer. Anal , vol.35 , pp. 2298-2316
    • BERGER, M.J.1    LEVEQUE, R.J.2
  • 11
    • 0036501622 scopus 로고    scopus 로고
    • A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions
    • D. CALHOUN, A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions, J. Comput. Phys., 176 (2002), pp. 231-275.
    • (2002) J. Comput. Phys , vol.176 , pp. 231-275
    • CALHOUN, D.1
  • 13
    • 0141758741 scopus 로고    scopus 로고
    • Solving the advection-diffusion equation in irregular geometries
    • D. CALHOUN AND R. J. LEVEQUE, Solving the advection-diffusion equation in irregular geometries, J. Comput. Phys., 156 (2000), pp. 1-38.
    • (2000) J. Comput. Phys , vol.156 , pp. 1-38
    • CALHOUN, D.1    LEVEQUE, R.J.2
  • 15
    • 56349138870 scopus 로고    scopus 로고
    • J. E. CASTILLO, ED., Mathematical Aspects of Numerical Grid Generation, Frontiers Appl. Math. 8, SIAM, Philadelphia, 1991.
    • J. E. CASTILLO, ED., Mathematical Aspects of Numerical Grid Generation, Frontiers Appl. Math. 8, SIAM, Philadelphia, 1991.
  • 16
    • 25444445567 scopus 로고    scopus 로고
    • A Cartesian grid embedded boundary method for hyperbolic conservation laws
    • P. COLELLA, D. T. GRAVES, B. J. KEEN, AND D. MODIANO, A Cartesian grid embedded boundary method for hyperbolic conservation laws, J. Comput. Phys., 211 (2006), pp. 347-366.
    • (2006) J. Comput. Phys , vol.211 , pp. 347-366
    • COLELLA, P.1    GRAVES, D.T.2    KEEN, B.J.3    MODIANO, D.4
  • 18
    • 0000397713 scopus 로고
    • A Lagrange multiplier approach for the metric terms of semi-Lagrangian models on the sphere
    • J. CÔTÉ, A Lagrange multiplier approach for the metric terms of semi-Lagrangian models on the sphere, Quart. J. R. Meteorol. Soc., 114 (1988), pp. 1347-1352.
    • (1988) Quart. J. R. Meteorol. Soc , vol.114 , pp. 1347-1352
    • CÔTÉ, J.1
  • 19
    • 28144436430 scopus 로고
    • An adaptively-refined Cartesian mesh solver for the Euler equations
    • D. DE ZEEUW AND K. POWELL, An adaptively-refined Cartesian mesh solver for the Euler equations, J. Comput. Phys., 104 (1993), pp. 56-68.
    • (1993) J. Comput. Phys , vol.104 , pp. 56-68
    • DE ZEEUW, D.1    POWELL, K.2
  • 20
    • 0000307275 scopus 로고    scopus 로고
    • A higher-order boundary treatment for Cartesian-grid methods
    • H. FORRER AND R. JELTSCH, A higher-order boundary treatment for Cartesian-grid methods, J. Comput. Phys., 140 (1998), pp. 259-277.
    • (1998) J. Comput. Phys , vol.140 , pp. 259-277
    • FORRER, H.1    JELTSCH, R.2
  • 21
    • 0035971808 scopus 로고    scopus 로고
    • A spectral element shallow water model on spherical geodesic grids
    • F. GIRALDO, A spectral element shallow water model on spherical geodesic grids, Internat. J. Numer. Methods Fluids, 35 (2001), pp. 869-901.
    • (2001) Internat. J. Numer. Methods Fluids , vol.35 , pp. 869-901
    • GIRALDO, F.1
  • 22
    • 0037144878 scopus 로고    scopus 로고
    • Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
    • F. GIRALDO, J. HESTHAVEN, AND T. WARBURTON, Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations, J. Comput. Phys., 181 (2002), pp. 499-525.
    • (2002) J. Comput. Phys , vol.181 , pp. 499-525
    • GIRALDO, F.1    HESTHAVEN, J.2    WARBURTON, T.3
  • 23
    • 18344391023 scopus 로고    scopus 로고
    • A nodal triangle-based spectral element method for the shallow water equations on the sphere
    • F. GIRALDO AND T. WARBURTON, A nodal triangle-based spectral element method for the shallow water equations on the sphere, J. Comput. Phys., 207 (2005), pp. 129-150.
    • (2005) J. Comput. Phys , vol.207 , pp. 129-150
    • GIRALDO, F.1    WARBURTON, T.2
  • 24
    • 0001346359 scopus 로고
    • The motion of atmospheric disturbances on the spherical earth
    • B. HAURWITZ, The motion of atmospheric disturbances on the spherical earth, J. Mar. Res., 3 (1940), pp. 254-267.
    • (1940) J. Mar. Res , vol.3 , pp. 254-267
    • HAURWITZ, B.1
  • 25
    • 19644394765 scopus 로고    scopus 로고
    • A high-resolution rotated grid method for conservation laws with embedded geometries
    • C. HELZEL, M. J. BERGER, AND R. J. LEVEQUE, A high-resolution rotated grid method for conservation laws with embedded geometries, SIAM J. Sci. Comput., 26 (2005), pp. 785-809.
    • (2005) SIAM J. Sci. Comput , vol.26 , pp. 785-809
    • HELZEL, C.1    BERGER, M.J.2    LEVEQUE, R.J.3
  • 26
    • 0346677456 scopus 로고    scopus 로고
    • An algorithm for aligning a quadrilateral grid with internal boundaries
    • J. M. HYMAN, S. LI, P. KNUPP, AND M. SHASHKOV, An algorithm for aligning a quadrilateral grid with internal boundaries, J. Comput. Phys., 163 (2000), pp. 133-149.
    • (2000) J. Comput. Phys , vol.163 , pp. 133-149
    • HYMAN, J.M.1    LI, S.2    KNUPP, P.3    SHASHKOV, M.4
  • 27
    • 0001827481 scopus 로고    scopus 로고
    • A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
    • H. JOHANSEN AND P. COLELLA, A Cartesian grid embedded boundary method for Poisson's equation on irregular domains, J. Comput. Phys., 147 (1998), pp. 60-85.
    • (1998) J. Comput. Phys , vol.147 , pp. 60-85
    • JOHANSEN, H.1    COLELLA, P.2
  • 30
    • 0012062674 scopus 로고    scopus 로고
    • A wave-propagation method for three-dimensional hyperbolic conservation laws
    • J. O. LANGSETH AND R. J. LEVEQUE, A wave-propagation method for three-dimensional hyperbolic conservation laws, J. Comput. Phys., 165 (2000), pp. 126-166.
    • (2000) J. Comput. Phys , vol.165 , pp. 126-166
    • LANGSETH, J.O.1    LEVEQUE, R.J.2
  • 31
    • 0348193014 scopus 로고    scopus 로고
    • Spatial discretization of the shallow water equations in spherical geometries
    • D. LANSER, J. BLOM, AND J. VERWER., Spatial discretization of the shallow water equations in spherical geometries, J. Comput. Phys., 165 (2000), pp. 542-565.
    • (2000) J. Comput. Phys , vol.165 , pp. 542-565
    • LANSER, D.1    BLOM, J.2    VERWER, J.3
  • 32
    • 2942543066 scopus 로고    scopus 로고
    • An immersed interface method for incompressible Navier-Stokes equations
    • L. LEE AND R. J. LEVEQUE, An immersed interface method for incompressible Navier-Stokes equations, SIAM J. Sci. Comput., 25 (2003), pp. 832-856.
    • (2003) SIAM J. Sci. Comput , vol.25 , pp. 832-856
    • LEE, L.1    LEVEQUE, R.J.2
  • 35
    • 0002258785 scopus 로고
    • High resolution finite volume methods on arbitrary grids via wave propagation
    • R. J. LEVEQUE, High resolution finite volume methods on arbitrary grids via wave propagation, J. Comput. Phys., 78 (1988), pp. 36-63.
    • (1988) J. Comput. Phys , vol.78 , pp. 36-63
    • LEVEQUE, R.J.1
  • 37
    • 56349160397 scopus 로고    scopus 로고
    • V. D. LISEIKIN, Grid Generation Methods, Sci. Comput., Springer-Verlag, Berlin, 1999.
    • V. D. LISEIKIN, Grid Generation Methods, Sci. Comput., Springer-Verlag, Berlin, 1999.
  • 38
    • 0021417514 scopus 로고
    • The fast solution of Poisson's and the biharmonic equations on irregular regions
    • A. MAYO, The fast solution of Poisson's and the biharmonic equations on irregular regions, SIAM J. Numer. Anal., 21 (1984), pp. 285-299.
    • (1984) SIAM J. Numer. Anal , vol.21 , pp. 285-299
    • MAYO, A.1
  • 39
    • 0000985731 scopus 로고
    • Fast parallel iterative solution of Poisson's and the biharmonic equations on irregular regions
    • A. MAYO AND A. GREENBAUM, Fast parallel iterative solution of Poisson's and the biharmonic equations on irregular regions, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 101-118.
    • (1992) SIAM J. Sci. Statist. Comput , vol.13 , pp. 101-118
    • MAYO, A.1    GREENBAUM, A.2
  • 40
    • 0030452194 scopus 로고    scopus 로고
    • A global shallow-water model using an expanded spherical cube: Gnonomic versus conformal coordinates
    • M. RANCIC, R. J. PURSER, AND F. MESSINGER, A global shallow-water model using an expanded spherical cube: Gnonomic versus conformal coordinates, Quart. J. R. Meteorol. Soc., 122 (1996), pp. 959-982.
    • (1996) Quart. J. R. Meteorol. Soc , vol.122 , pp. 959-982
    • RANCIC, M.1    PURSER, R.J.2    MESSINGER, F.3
  • 41
    • 0030096121 scopus 로고    scopus 로고
    • The "cubed sphere": A new method for the solution of partial differential equations in spherical geometry
    • C. RONCHI, R. IACONO, AND P. S. PAOLUCCI, The "cubed sphere": A new method for the solution of partial differential equations in spherical geometry, J. Comput. Phys., 124 (1996), pp. 93-114.
    • (1996) J. Comput. Phys , vol.124 , pp. 93-114
    • RONCHI, C.1    IACONO, R.2    PAOLUCCI, P.S.3
  • 43
    • 32644450000 scopus 로고    scopus 로고
    • A wave propagation method for hyperbolic systems on the sphere
    • J. A. ROSSMANITH, A wave propagation method for hyperbolic systems on the sphere, J. Comput. Phys., 213 (2006), pp. 629-658.
    • (2006) J. Comput. Phys , vol.213 , pp. 629-658
    • ROSSMANITH, J.A.1
  • 44
    • 4544271886 scopus 로고
    • Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids
    • R. SADOURNY, Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids, Monthly Weather Rev., 100 (1972), pp. 211-224.
    • (1972) Monthly Weather Rev , vol.100 , pp. 211-224
    • SADOURNY, R.1
  • 45
    • 0000184292 scopus 로고
    • Integration of a non-divergent barotropic vorticity equation with an icosahedral-hexagonal grid for the sphere
    • R. SADOURNY, A. ARAKAWA, AND Y. MINTZ, Integration of a non-divergent barotropic vorticity equation with an icosahedral-hexagonal grid for the sphere, Monthly Weather Rev., 96 (1968), pp. 351-356.
    • (1968) Monthly Weather Rev , vol.96 , pp. 351-356
    • SADOURNY, R.1    ARAKAWA, A.2    MINTZ, Y.3
  • 46
    • 0032473230 scopus 로고    scopus 로고
    • B. SOMMEIJER, L. SHAMPINE, AND J. VERWER, RKC: An explicit solver for parabolic PDEs, J. Comput. Appl. Math., 88 (1997), pp. 315-326.
    • B. SOMMEIJER, L. SHAMPINE, AND J. VERWER, RKC: An explicit solver for parabolic PDEs, J. Comput. Appl. Math., 88 (1997), pp. 315-326.
  • 47
    • 0034079274 scopus 로고    scopus 로고
    • Numerical simulations of Rossby-Haurwitz waves
    • J. THUBURN AND Y. LI, Numerical simulations of Rossby-Haurwitz waves, Tellus, 52A (2000), pp. 181-189.
    • (2000) Tellus , vol.52 A , pp. 181-189
    • THUBURN, J.1    LI, Y.2
  • 48
    • 0033215734 scopus 로고    scopus 로고
    • Turing patterns on a sphere
    • C. VAREA, J. ARAGON, AND R. BARRIO, Turing patterns on a sphere, Phys. Rev. E, 60 (1999), pp. 4588-4592.
    • (1999) Phys. Rev. E , vol.60 , pp. 4588-4592
    • VAREA, C.1    ARAGON, J.2    BARRIO, R.3
  • 49
    • 0001440358 scopus 로고
    • A standard test set for numerical approximations to the shallow water equations in spherical geometry
    • D. WILLIAMSON, J. DRAKE, J. HACK, R. JAKOB, AND P. SWARZTRAUBER, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys., 102 (1992), pp. 211-224.
    • (1992) J. Comput. Phys , vol.102 , pp. 211-224
    • WILLIAMSON, D.1    DRAKE, J.2    HACK, J.3    JAKOB, R.4    SWARZTRAUBER, P.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.