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Volumn 153, Issue 3, 2003, Pages 317-339

Adaptive mesh refinement for conservative systems: Multi-dimensional efficiency evaluation

Author keywords

Adaptive Mesh Refinement; Computational efficiency; Conservation laws; Magnetohydrodynamics; Shock capturing

Indexed keywords

COMPUTER SIMULATION; CONSERVATION; MAGNETOHYDRODYNAMICS;

EID: 0038487249     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-4655(03)00139-5     Document Type: Article
Times cited : (162)

References (53)
  • 1
    • 0008688174 scopus 로고    scopus 로고
    • A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations
    • Almgren A.S., Bell J.B., Colella P., Howell L.H., Welcome M.L. A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J. Comput. Phys. 142:1998;1.
    • (1998) J. Comput. Phys. , vol.142 , pp. 1
    • Almgren, A.S.1    Bell, J.B.2    Colella, P.3    Howell, L.H.4    Welcome, M.L.5
  • 2
    • 0035842859 scopus 로고    scopus 로고
    • Divergence-free adaptive mesh refinement for magnetohydrodynamics
    • Balsara D.S. Divergence-free adaptive mesh refinement for magnetohydrodynamics. J. Comput. Phys. 174:2001;614.
    • (2001) J. Comput. Phys. , vol.174 , pp. 614
    • Balsara, D.S.1
  • 3
    • 0001690874 scopus 로고    scopus 로고
    • A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations
    • Balsara D.S., Spicer D.S. A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations. J. Comput. Phys. 149:1999;270.
    • (1999) J. Comput. Phys. , vol.149 , pp. 270
    • Balsara, D.S.1    Spicer, D.S.2
  • 4
    • 0000843403 scopus 로고
    • Three-dimensional adaptive mesh refinement for hyperbolic conservation laws
    • Bell J., Berger M., Saltzman J., Welcome M. Three-dimensional adaptive mesh refinement for hyperbolic conservation laws. SIAM J. Sci. Comput. 15:1994;127.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 127
    • Bell, J.1    Berger, M.2    Saltzman, J.3    Welcome, M.4
  • 5
    • 0001608079 scopus 로고
    • A second-order projection method for the incompressible Navier-Stokes equations
    • Bell J.B., Colella P., Glaz H.M. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85:1989;257.
    • (1989) J. Comput. Phys. , vol.85 , pp. 257
    • Bell, J.B.1    Colella, P.2    Glaz, H.M.3
  • 6
    • 0005310928 scopus 로고
    • Data structures for adaptive grid generation
    • Berger M.J. Data structures for adaptive grid generation. SIAM J. Sci. Stat. Comput. 7:1986;904.
    • (1986) SIAM J. Sci. Stat. Comput. , vol.7 , pp. 904
    • Berger, M.J.1
  • 7
    • 11744289966 scopus 로고
    • Local adaptive mesh refinement for shock hydrodynamics
    • Berger M.J., Colella P. Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82:1989;64.
    • (1989) J. Comput. Phys. , vol.82 , pp. 64
    • Berger, M.J.1    Colella, P.2
  • 8
    • 0001762370 scopus 로고    scopus 로고
    • Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems
    • Berger M.J., LeVeque R.J. Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems. SIAM J. Numer. Anal. 35:1998;2298.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2298
    • Berger, M.J.1    LeVeque, R.J.2
  • 11
    • 33749583060 scopus 로고
    • Flux-corrected transport. I. SHASTA, A fluid transport algorithm that works
    • Boris J.P., Book D.L. Flux-corrected transport. I. SHASTA, A fluid transport algorithm that works. J. Comput. Phys. 11:1973;38.
    • (1973) J. Comput. Phys. , vol.11 , pp. 38
    • Boris, J.P.1    Book, D.L.2
  • 12
    • 0001689247 scopus 로고
    • The effect of nonzero ▽ · B on the numerical solution of the magnetohydrodynamic equations
    • Brackbill J.U., Barnes D.C. The effect of nonzero ▽·B on the numerical solution of the magnetohydrodynamic equations. J. Comput. Phys. 35:1980;426.
    • (1980) J. Comput. Phys. , vol.35 , pp. 426
    • Brackbill, J.U.1    Barnes, D.C.2
  • 13
    • 45449121905 scopus 로고
    • An upwind differencing scheme for the equations of ideal magnetohydrodynamics
    • Brio M., Wu C.C. An upwind differencing scheme for the equations of ideal magnetohydrodynamics. J. Comput. Phys. 75:1988;400.
    • (1988) J. Comput. Phys. , vol.75 , pp. 400
    • Brio, M.1    Wu, C.C.2
  • 14
    • 0008391610 scopus 로고
    • Simulation of unsteady inviscid flow on an adaptively refined Cartesian grid
    • Chiang Y.-L., van Leer B., Powell K.G. Simulation of unsteady inviscid flow on an adaptively refined Cartesian grid. AIAA. 92-0443:1992.
    • (1992) AIAA , vol.92 , Issue.443
    • Chiang, Y.-L.1    Van Leer, B.2    Powell, K.G.3
  • 15
    • 0035455630 scopus 로고    scopus 로고
    • A note on magnetic monopolies and the one-dimensional MHD Riemann problem
    • Dellar P.J. A note on magnetic monopolies and the one-dimensional MHD Riemann problem. J. Comput. Phys. 172:2001;392.
    • (2001) J. Comput. Phys. , vol.172 , pp. 392
    • Dellar, P.J.1
  • 17
    • 0031161659 scopus 로고    scopus 로고
    • Adaptive mesh refinement for singular current sheets in incompressible magnetohydrodynamic flows
    • Friedel H., Grauer R., Marliani C. Adaptive mesh refinement for singular current sheets in incompressible magnetohydrodynamic flows. J. Comput. Phys. 134:1997;190.
    • (1997) J. Comput. Phys. , vol.134 , pp. 190
    • Friedel, H.1    Grauer, R.2    Marliani, C.3
  • 18
    • 0000383154 scopus 로고    scopus 로고
    • Adaptive mesh and algorithm refinement using direct simulation Monte Carlo
    • Garcia A.L., Bell J.B., Crutchfield W.Y., Alder B.J. Adaptive mesh and algorithm refinement using direct simulation Monte Carlo. J. Comput. Phys. 154:1999;134.
    • (1999) J. Comput. Phys. , vol.154 , pp. 134
    • Garcia, A.L.1    Bell, J.B.2    Crutchfield, W.Y.3    Alder, B.J.4
  • 19
    • 40749159424 scopus 로고
    • High resolution schemes for hyperbolic conservation laws
    • Harten A. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49:1983;357.
    • (1983) J. Comput. Phys. , vol.49 , pp. 357
    • Harten, A.1
  • 20
    • 0001388659 scopus 로고    scopus 로고
    • A positive conservative method for magnetohydrodynamics based on HLL and Roe methods
    • Janhunen P. A positive conservative method for magnetohydrodynamics based on HLL and Roe methods. J. Comput. Phys. 160:2000;649.
    • (2000) J. Comput. Phys. , vol.160 , pp. 649
    • Janhunen, P.1
  • 22
    • 84944036372 scopus 로고    scopus 로고
    • Simulating magnetized plasma with the versatile advection code
    • Keppens R., Tóth G. Simulating magnetized plasma with the Versatile Advection Code. Lecture Notes in Comput. Sci. 1573:1999;680.
    • (1999) Lecture Notes in Comput. Sci. , vol.1573 , pp. 680
    • Keppens, R.1    Tóth, G.2
  • 23
    • 0343007351 scopus 로고    scopus 로고
    • Using high performance Fortran for magnetohydrodynamic simulations
    • Keppens R., Tóth G. Using high performance Fortran for magnetohydrodynamic simulations. Parallel Comput. 26:2000;705.
    • (2000) Parallel Comput. , vol.26 , pp. 705
    • Keppens, R.1    Tóth, G.2
  • 25
    • 0344339061 scopus 로고    scopus 로고
    • Growth and saturation of the Kelvin-Helmholtz instability with parallel and antiparallel magnetic fields
    • Keppens R., Tóth G., Westermann R.H.J., Goedbloed J.P. Growth and saturation of the Kelvin-Helmholtz instability with parallel and antiparallel magnetic fields. J. Plasma Phys. 61:1999;1.
    • (1999) J. Plasma Phys. , vol.61 , pp. 1
    • Keppens, R.1    Tóth, G.2    Westermann, R.H.J.3    Goedbloed, J.P.4
  • 27
    • 23044534854 scopus 로고    scopus 로고
    • OpenMP parallelism for multi-dimensional grid-adaptive magnetohydrodynamic simulations
    • Keppens R., Tóth G. OpenMP parallelism for multi-dimensional grid-adaptive magnetohydrodynamic simulations. Lecture Notes in Comput. Sci. 2329:2002;940.
    • (2002) Lecture Notes in Comput. Sci. , vol.2329 , pp. 940
    • Keppens, R.1    Tóth, G.2
  • 28
    • 0012062674 scopus 로고    scopus 로고
    • A wave propagation method for three-dimensional hyperbolic conservation laws
    • Langseth J.O., LeVeque R.J. A wave propagation method for three-dimensional hyperbolic conservation laws. J. Comput. Phys. 165:2000;126.
    • (2000) J. Comput. Phys. , vol.165 , pp. 126
    • Langseth, J.O.1    LeVeque, R.J.2
  • 30
    • 0000308880 scopus 로고    scopus 로고
    • Wave propagation algorithms for multi-dimensional hyperbolic systems
    • LeVeque R.J. Wave propagation algorithms for multi-dimensional hyperbolic systems. J. Comput. Phys. 131:1997;327.
    • (1997) J. Comput. Phys. , vol.131 , pp. 327
    • LeVeque, R.J.1
  • 32
    • 0002300781 scopus 로고
    • A method for incorporating Gauss' law into electromagnetic PIC codes
    • Marder B. A method for incorporating Gauss' law into electromagnetic PIC codes. J. Comput. Phys. 68:1987;48.
    • (1987) J. Comput. Phys. , vol.68 , pp. 48
    • Marder, B.1
  • 33
    • 0038090587 scopus 로고    scopus 로고
    • AMRVAC: A multi-dimensional grid-adaptive magnetofluid dynamics code
    • Nool M., Keppens R. AMRVAC: a multi-dimensional grid-adaptive magnetofluid dynamics code. Comput. Methods Appl. Math. 2:2002;92.
    • (2002) Comput. Methods Appl. Math. , vol.2 , pp. 92
    • Nool, M.1    Keppens, R.2
  • 34
    • 0018286867 scopus 로고
    • Small-scale structure of two-dimensional magnetohydrodynamic turbulence
    • Orszag A., Tang C.M. Small-scale structure of two-dimensional magnetohydrodynamic turbulence. J. Fluid Mech. 90:1979;129.
    • (1979) J. Fluid Mech. , vol.90 , pp. 129
    • Orszag, A.1    Tang, C.M.2
  • 35
    • 0002634491 scopus 로고
    • Evolution of the Orszag-Tang vortex system in a compressible medium. II. Supersonic flow
    • Picone J.M., Dahlburg R.B. Evolution of the Orszag-Tang vortex system in a compressible medium. II. Supersonic flow. Phys. Fluids B. 3:1991;29.
    • (1991) Phys. Fluids B , vol.3 , pp. 29
    • Picone, J.M.1    Dahlburg, R.B.2
  • 36
    • 0003243194 scopus 로고
    • An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension)
    • Langley, VA
    • K.G. Powell, An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension), ICASE Report No 94-24, Langley, VA, 1994.
    • (1994) ICASE Report No 94-24 , vol.94 , Issue.24
    • Powell, K.G.1
  • 38
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors, and difference schemes
    • Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43:1981;357.
    • (1981) J. Comput. Phys. , vol.43 , pp. 357
    • Roe, P.L.1
  • 39
    • 0030087226 scopus 로고    scopus 로고
    • Notes on the eigensystem of magnetohydrodynamics
    • Roe P.L., Balsara D.S. Notes on the eigensystem of magnetohydrodynamics. SIAM J. Appl. Math. 56:1996;57.
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 57
    • Roe, P.L.1    Balsara, D.S.2
  • 40
    • 0009293999 scopus 로고
    • Dynamic interaction of convection with magnetic flux sheets: First results of a new MHD code
    • R.J. Rutten, & C.J. Schrijver. Dordrecht: Kluwer
    • Steiner O., Knölker M., Schüssler M. Dynamic interaction of convection with magnetic flux sheets: first results of a new MHD code. Rutten R.J., Schrijver C.J. Solar Surface Magnetism. 1993;Kluwer, Dordrecht.
    • (1993) Solar Surface Magnetism
    • Steiner, O.1    Knölker, M.2    Schüssler, M.3
  • 41
    • 0001518684 scopus 로고
    • On the construction and comparison of difference schemes
    • Strang G. On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5:1968;506.
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 506
    • Strang, G.1
  • 42
    • 0346046827 scopus 로고    scopus 로고
    • The ▽ · B = 0 constraint in shock-capturing magnetohydrodynamic codes
    • Tóth G. The ▽·B=0 constraint in shock-capturing magnetohydrodynamic codes. J. Comput. Phys. 161:2000;605.
    • (2000) J. Comput. Phys. , vol.161 , pp. 605
    • Tóth, G.1
  • 43
    • 0002960399 scopus 로고    scopus 로고
    • The LASY preprocessor and its application to general multi-dimensional codes
    • Tóth G. The LASY preprocessor and its application to general multi-dimensional codes. J. Comput. Phys. 138:1997;981.
    • (1997) J. Comput. Phys. , vol.138 , pp. 981
    • Tóth, G.1
  • 44
    • 21444448345 scopus 로고    scopus 로고
    • A general code for modeling MHD flows on parallel computers: Versatile advection code
    • Tóth G. A general code for modeling MHD flows on parallel computers: Versatile Advection Code. Astrophys. Lett. Comm. 34:1996;245 http://www.phys.uu.nl/̃toth.
    • (1996) Astrophys. Lett. Comm. , vol.34 , pp. 245
    • Tóth, G.1
  • 45
    • 0001085487 scopus 로고    scopus 로고
    • Implicit and semi-implicit schemes in the versatile advection code: Numerical tests
    • Tóth G., Keppens R., Botchev M.A. Implicit and semi-implicit schemes in the Versatile Advection Code: numerical tests. Astron. Astrophys. 332:1998;1159.
    • (1998) Astron. Astrophys. , vol.332 , pp. 1159
    • Tóth, G.1    Keppens, R.2    Botchev, M.A.3
  • 46
    • 0030268703 scopus 로고    scopus 로고
    • Comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems
    • Tóth G., Odstrčil D. Comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems. J. Comput. Phys. 128:1996;82.
    • (1996) J. Comput. Phys. , vol.128 , pp. 82
    • Tóth, G.1    Odstrčil, D.2
  • 47
    • 0037055773 scopus 로고    scopus 로고
    • Divergence- and curl-preserving prolongation and restriction formulas
    • Tóth G., Roe P.L. Divergence- and curl-preserving prolongation and restriction formulas. J. Comput. Phys. 180:2002;736.
    • (2002) J. Comput. Phys. , vol.180 , pp. 736
    • Tóth, G.1    Roe, P.L.2
  • 48
    • 2442433925 scopus 로고
    • Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's method
    • van Leer B. Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's method. J. Comput. Phys. 32:1979;101.
    • (1979) J. Comput. Phys. , vol.32 , pp. 101
    • Van Leer, B.1
  • 49
    • 0001329071 scopus 로고    scopus 로고
    • A-MAZE: A code package to compute 3D magnetic flows, 3D NLTE radiative transfer, and synthetic spectra
    • Thermal and Ionization Aspects of Flows from Hot Stars: Observations and Theory
    • Walder R., Folini D. A-MAZE: A code package to compute 3D magnetic flows, 3D NLTE radiative transfer, and synthetic spectra. Thermal and Ionization Aspects of Flows from Hot Stars: Observations and Theory. ASP Conference Series. 204:2000;281.
    • (2000) ASP Conference Series , vol.204 , pp. 281
    • Walder, R.1    Folini, D.2
  • 50
    • 0000219229 scopus 로고    scopus 로고
    • Colliding winds in WR binaries: Further developments within a complicated story
    • K.A. van der Hucht, G. Koenigsberger, & P.R.J. Eenens.
    • Walder R., Folini D., Motamen S. Colliding winds in WR binaries: further developments within a complicated story. van der Hucht K.A., Koenigsberger G., Eenens P.R.J. Proc. IAU Symposium, No. 193. 1999;298.
    • (1999) Proc. IAU Symposium, No. 193 , vol.193 , pp. 298
    • Walder, R.1    Folini, D.2    Motamen, S.3
  • 51
    • 48749139407 scopus 로고
    • The numerical simulation of two-dimensional fluid flow with strong shocks
    • Woodward P.R., Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54:1984;115.
    • (1984) J. Comput. Phys. , vol.54 , pp. 115
    • Woodward, P.R.1    Colella, P.2
  • 53
    • 0032714391 scopus 로고    scopus 로고
    • A three-dimensional Cartesian adaptive mesh code for compressible magnetohydrodynamics
    • Ziegler U. A three-dimensional Cartesian adaptive mesh code for compressible magnetohydrodynamics. Comput. Phys. Commun. 116:1999;65.
    • (1999) Comput. Phys. Commun. , vol.116 , pp. 65
    • Ziegler, U.1


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