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Volumn 231, Issue 14, 2012, Pages 4723-4744

Mass, momentum and energy conserving (MaMEC) discretizations on general grids for the compressible Euler and shallow water equations

Author keywords

CFD; Compressible euler equations; Energy conserving discretization; Shallow water equations; Staggered grid

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; ENERGY CONSERVATION; EQUATIONS OF MOTION; FINITE VOLUME METHOD; MOMENTUM;

EID: 84861226582     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.03.005     Document Type: Article
Times cited : (36)

References (39)
  • 1
    • 33744482805 scopus 로고
    • Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow
    • Arakawa A. Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. J. Comput. Phys. 1966, 1:119-143.
    • (1966) J. Comput. Phys. , vol.1 , pp. 119-143
    • Arakawa, A.1
  • 2
    • 15744375750 scopus 로고    scopus 로고
    • A semi-implicit method conserving mass and potential vorticity for the shallow water equations on the sphere
    • Bonaventura L., Kornblueh L., Heinze T., Ripodas P. A semi-implicit method conserving mass and potential vorticity for the shallow water equations on the sphere. Int. J. Numer. Methods Fluids 2005, 47:863-869.
    • (2005) Int. J. Numer. Methods Fluids , vol.47 , pp. 863-869
    • Bonaventura, L.1    Kornblueh, L.2    Heinze, T.3    Ripodas, P.4
  • 3
    • 0000142136 scopus 로고    scopus 로고
    • The construction of compatible hydrodynamics algorithms utilizing conservation of total energy
    • Caramana E.J., Burton D.E., Shashkov M.J., Whalen P.P. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy. J. Comput. Phys. 1998, 146:227-262.
    • (1998) J. Comput. Phys. , vol.146 , pp. 227-262
    • Caramana, E.J.1    Burton, D.E.2    Shashkov, M.J.3    Whalen, P.P.4
  • 4
    • 15744374843 scopus 로고    scopus 로고
    • A new symmetry-preserving Cartesian-grid method for computing flow past arbitrarily shaped objects
    • Dröge M., Verstappen R. A new symmetry-preserving Cartesian-grid method for computing flow past arbitrarily shaped objects. Int. J. Numer. Methods Fluids 2005, 47:979-985.
    • (2005) Int. J. Numer. Methods Fluids , vol.47 , pp. 979-985
    • Dröge, M.1    Verstappen, R.2
  • 5
    • 0001395296 scopus 로고    scopus 로고
    • High-order fluxes for conservative skew-symmetric-like schemes in structured meshes: application to compressible flows
    • Ducros F., Laporte F., Souléres T., Guinot V., Moinat P., Caruelle B. High-order fluxes for conservative skew-symmetric-like schemes in structured meshes: application to compressible flows. J. Comput. Phys. 2000, 161:114-139.
    • (2000) J. Comput. Phys. , vol.161 , pp. 114-139
    • Ducros, F.1    Laporte, F.2    Souléres, T.3    Guinot, V.4    Moinat, P.5    Caruelle, B.6
  • 6
    • 74449083633 scopus 로고    scopus 로고
    • Statistical relevance of vorticity conservation in the Hamiltonian particle-mesh method
    • Dubinkina S., Frank J. Statistical relevance of vorticity conservation in the Hamiltonian particle-mesh method. J. Comput. Phys. 2010, 229:2634-2648.
    • (2010) J. Comput. Phys. , vol.229 , pp. 2634-2648
    • Dubinkina, S.1    Frank, J.2
  • 7
    • 1542543685 scopus 로고
    • Numerical simulation of a compressible, homogeneous, turbulent shear flow
    • Report TF-13, Thermosciences Division, Mechanical Engineering, Stanford University.
    • W.J. Feiereisen, W.C. Reynolds, J.H. Ferziger, Numerical simulation of a compressible, homogeneous, turbulent shear flow. Report TF-13, Thermosciences Division, Mechanical Engineering, Stanford University, 1981.
    • (1981)
    • Feiereisen, W.J.1    Reynolds, W.C.2    Ferziger, J.H.3
  • 8
    • 33645956789 scopus 로고    scopus 로고
    • Kinetic energy conservation issues associated with the collocated mesh scheme for incompressible flow
    • Felten F.N., Lund T.S. Kinetic energy conservation issues associated with the collocated mesh scheme for incompressible flow. J. Comput. Phys. 2006, 215:465-484.
    • (2006) J. Comput. Phys. , vol.215 , pp. 465-484
    • Felten, F.N.1    Lund, T.S.2
  • 9
    • 4043081955 scopus 로고    scopus 로고
    • Conservation properties of smoothed particle hydrodynamics applied to the shallow water equations
    • Frank J., Reich S. Conservation properties of smoothed particle hydrodynamics applied to the shallow water equations. BIT Numer. Methods 2003, 43:40-54.
    • (2003) BIT Numer. Methods , vol.43 , pp. 40-54
    • Frank, J.1    Reich, S.2
  • 10
    • 38349016685 scopus 로고    scopus 로고
    • The construction of discretely conservative finite volume schemes that also globally conserve energy or entropy
    • Jameson A. The construction of discretely conservative finite volume schemes that also globally conserve energy or entropy. J. Sci. Comput. 2008, 234:152-187.
    • (2008) J. Sci. Comput. , vol.234 , pp. 152-187
    • Jameson, A.1
  • 11
    • 84861229162 scopus 로고    scopus 로고
    • A robust scheme for compressible flows with a minimum artificial stabilization
    • Annual Research Briefs 2009, Center for Turbulent Research, Stanford University
    • S. Kang, H. Pitsch, A robust scheme for compressible flows with a minimum artificial stabilization. Annual Research Briefs 2009, Center for Turbulent Research, Stanford University, 2009, pp. 353-365.
    • (2009) , pp. 353-365
    • Kang, S.1    Pitsch, H.2
  • 12
    • 21844453231 scopus 로고    scopus 로고
    • Cosymmetry preserving finite-difference methods for convection equations in a porous medium
    • Karasözen B., Tsybulin V.G. Cosymmetry preserving finite-difference methods for convection equations in a porous medium. Appl. Numer. Math. 2005, 55:69-82.
    • (2005) Appl. Numer. Math. , vol.55 , pp. 69-82
    • Karasözen, B.1    Tsybulin, V.G.2
  • 14
    • 67849119401 scopus 로고    scopus 로고
    • A high-order low-dispersion symmetry-preserving finite-volume method for compressible flow on curvilinear grids
    • Kok J.C. A high-order low-dispersion symmetry-preserving finite-volume method for compressible flow on curvilinear grids. J. Comput. Phys. 2009, 228:6811-6832.
    • (2009) J. Comput. Phys. , vol.228 , pp. 6811-6832
    • Kok, J.C.1
  • 15
    • 4544328546 scopus 로고    scopus 로고
    • Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry
    • Liu J.-G., Wang W.-C. Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry. J. Comput. Phys. 2004, 200:8-33.
    • (2004) J. Comput. Phys. , vol.200 , pp. 8-33
    • Liu, J.-G.1    Wang, W.-C.2
  • 16
    • 0003618878 scopus 로고
    • Numerical methods used in atmospheric models
    • Mesinger F., Arakawa A. Numerical methods used in atmospheric models. GARP Publ. Ser. 1977, 1(17).
    • (1977) GARP Publ. Ser. , vol.1 , Issue.17
    • Mesinger, F.1    Arakawa, A.2
  • 17
    • 77955273607 scopus 로고    scopus 로고
    • Skew-symmetric form of convective terms and fully conservative finite difference schemes for variable density low-Mach number flows
    • Morinishi Y. Skew-symmetric form of convective terms and fully conservative finite difference schemes for variable density low-Mach number flows. J. Comput. Phys. 2010, 229:276-300.
    • (2010) J. Comput. Phys. , vol.229 , pp. 276-300
    • Morinishi, Y.1
  • 18
    • 0002414440 scopus 로고    scopus 로고
    • Fully conservative finite difference schemes for incompressible flow
    • Morinishi Y., Lund T.S., Vasilyev O.V., Moin P. Fully conservative finite difference schemes for incompressible flow. J. Comput. Phys. 1998, 143:90-124.
    • (1998) J. Comput. Phys. , vol.143 , pp. 90-124
    • Morinishi, Y.1    Lund, T.S.2    Vasilyev, O.V.3    Moin, P.4
  • 19
    • 0002868129 scopus 로고    scopus 로고
    • Conservation properties of unstructured staggered mesh schemes
    • Perot B. Conservation properties of unstructured staggered mesh schemes. J. Comput. Phys. 2000, 159:58-89.
    • (2000) J. Comput. Phys. , vol.159 , pp. 58-89
    • Perot, B.1
  • 20
    • 79951967877 scopus 로고    scopus 로고
    • Discrete conservation properties of unstructured mesh schemes
    • Blair Perot J. Discrete conservation properties of unstructured mesh schemes. Ann. Rev. Fluid Mech. 2011, 43:299-318.
    • (2011) Ann. Rev. Fluid Mech. , vol.43 , pp. 299-318
    • Blair Perot, J.1
  • 21
    • 34248187094 scopus 로고    scopus 로고
    • Discrete calculus methods for diffusion
    • Perot B., Subramanian V. Discrete calculus methods for diffusion. J. Comput. Phys. 2007, 224:59-81.
    • (2007) J. Comput. Phys. , vol.224 , pp. 59-81
    • Perot, B.1    Subramanian, V.2
  • 22
    • 0001518767 scopus 로고
    • Conservation properties of convection difference schemes
    • Piacsek S.A., Williams G.P. Conservation properties of convection difference schemes. J. Comput. Phys. 1970, 6:392-405.
    • (1970) J. Comput. Phys. , vol.6 , pp. 392-405
    • Piacsek, S.A.1    Williams, G.P.2
  • 23
    • 79954880560 scopus 로고    scopus 로고
    • A mimetic mass, momentum and energy conserving discretization for the shallow water equations
    • van Reeuwijk M. A mimetic mass, momentum and energy conserving discretization for the shallow water equations. Comput. Fluids 2011, 46:411-416.
    • (2011) Comput. Fluids , vol.46 , pp. 411-416
    • van Reeuwijk, M.1
  • 24
    • 0036566625 scopus 로고    scopus 로고
    • A potential enstrophy and energy conserving numerical scheme for solution of the shallow water equations on a geodesic grid
    • Ringler Todd D., Randall David A. A potential enstrophy and energy conserving numerical scheme for solution of the shallow water equations on a geodesic grid. Mon. Weath. Rev. 2002, 130:1397-1410.
    • (2002) Mon. Weath. Rev. , vol.130 , pp. 1397-1410
    • Ringler, T.D.1    Randall, D.A.2
  • 25
    • 84992377190 scopus 로고    scopus 로고
    • A discrete calculus with applications of high-order discretizations to boundary-value problems
    • Steinberg S. A discrete calculus with applications of high-order discretizations to boundary-value problems. Comput. Methods Appl. Math. 2004, 4:228-261.
    • (2004) Comput. Methods Appl. Math. , vol.4 , pp. 228-261
    • Steinberg, S.1
  • 26
    • 0345790331 scopus 로고    scopus 로고
    • A staggered conservative scheme for every Froude number in rapidly varied shallow water flows
    • Stelling G.S., Duinmeijer S.P.A. A staggered conservative scheme for every Froude number in rapidly varied shallow water flows. Int. J. Numer. Methods Fluids 2003, 43:1329-1354.
    • (2003) Int. J. Numer. Methods Fluids , vol.43 , pp. 1329-1354
    • Stelling, G.S.1    Duinmeijer, S.P.A.2
  • 27
    • 0002449864 scopus 로고
    • Summation by parts for finite difference approximations for d/dx
    • Strand B. Summation by parts for finite difference approximations for d/dx. J. Comput. Phys. 1994, 110:47-67.
    • (1994) J. Comput. Phys. , vol.110 , pp. 47-67
    • Strand, B.1
  • 28
    • 58649086284 scopus 로고    scopus 로고
    • A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows
    • Subbareddy P.K., Candler G.V. A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows. J. Comput. Phys. 2009, 228:1347-1384.
    • (2009) J. Comput. Phys. , vol.228 , pp. 1347-1384
    • Subbareddy, P.K.1    Candler, G.V.2
  • 29
    • 33750299447 scopus 로고    scopus 로고
    • Higher-order mimetic methods for unstructured meshes
    • Subramanian V., Perot B. Higher-order mimetic methods for unstructured meshes. J. Comput. Phys. 2006, 219:68-85.
    • (2006) J. Comput. Phys. , vol.219 , pp. 68-85
    • Subramanian, V.1    Perot, B.2
  • 30
    • 77956343958 scopus 로고    scopus 로고
    • Parameter-free symmetry-preserving regularization modeling of a turbulent differentially heated cavity
    • Trias F.X., Verstappen R.W.C.P., Gorobets A., Soria M., Oliva A. Parameter-free symmetry-preserving regularization modeling of a turbulent differentially heated cavity. Comput. Fluids 2010, 39:1815-1831.
    • (2010) Comput. Fluids , vol.39 , pp. 1815-1831
    • Trias, F.X.1    Verstappen, R.W.C.P.2    Gorobets, A.3    Soria, M.4    Oliva, A.5
  • 31
    • 0034687916 scopus 로고    scopus 로고
    • High order difference schemes on non-uniform meshes with good conservation properties
    • Vasilyev O.V. High order difference schemes on non-uniform meshes with good conservation properties. J. Comput. Phys. 2000, 157:746-761.
    • (2000) J. Comput. Phys. , vol.157 , pp. 746-761
    • Vasilyev, O.V.1
  • 32
    • 52949102994 scopus 로고    scopus 로고
    • Symmetry-preserving upwind discretization of convection on non-uniform grids
    • Veldman A.E.P., Lam K.-W. Symmetry-preserving upwind discretization of convection on non-uniform grids. Appl. Numer. Math. 2008, 58:1881-1891.
    • (2008) Appl. Numer. Math. , vol.58 , pp. 1881-1891
    • Veldman, A.E.P.1    Lam, K.-W.2
  • 33
    • 33751536389 scopus 로고
    • Playing with nonuniform grids
    • Veldman A.E.P., Rinzema K. Playing with nonuniform grids. J. Eng. Math. 1991, 26:119-130.
    • (1991) J. Eng. Math. , vol.26 , pp. 119-130
    • Veldman, A.E.P.1    Rinzema, K.2
  • 35
    • 43649104777 scopus 로고    scopus 로고
    • On restraining the production of small scales of motion in a turbulent channel flow
    • Verstappen R. On restraining the production of small scales of motion in a turbulent channel flow. Comput. Fluids 2008, 37:887-897.
    • (2008) Comput. Fluids , vol.37 , pp. 887-897
    • Verstappen, R.1
  • 36
    • 0031251953 scopus 로고    scopus 로고
    • Direct numerical simulation of turbulence at lesser costs
    • Verstappen R.W.C.P., Veldman A.E.P. Direct numerical simulation of turbulence at lesser costs. J. Eng. Math. 1997, 32:143-159.
    • (1997) J. Eng. Math. , vol.32 , pp. 143-159
    • Verstappen, R.W.C.P.1    Veldman, A.E.P.2
  • 37
    • 0032128507 scopus 로고    scopus 로고
    • Spectro-consistent discretization: a challenge to RANS and LES
    • Verstappen R.W.C.P., Veldman A.E.P. Spectro-consistent discretization: a challenge to RANS and LES. J. Eng. Math. 1998, 34:163-179.
    • (1998) J. Eng. Math. , vol.34 , pp. 163-179
    • Verstappen, R.W.C.P.1    Veldman, A.E.P.2
  • 38
    • 0037407582 scopus 로고    scopus 로고
    • Symmetry-preserving discretization of turbulent flow
    • Verstappen R.W.C.P., Veldman A.E.P. Symmetry-preserving discretization of turbulent flow. J. Comput. Phys. 2003, 187:343-368.
    • (2003) J. Comput. Phys. , vol.187 , pp. 343-368
    • Verstappen, R.W.C.P.1    Veldman, A.E.P.2
  • 39
    • 73849087153 scopus 로고    scopus 로고
    • Numerical simulation of two-phase flow in offshore environments
    • PhD Thesis, University of Groningen, The Netherlands
    • R. Wemmenhove. Numerical simulation of two-phase flow in offshore environments. PhD Thesis, University of Groningen, The Netherlands, 2008.
    • (2008)
    • Wemmenhove, R.1


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