메뉴 건너뛰기




Volumn 63, Issue 6, 2003, Pages 2020-2041

Low Mach number flows in time-dependent domains

(1)  Ali G a  

a CNR   (Italy)

Author keywords

Asymptotic analysis; Euler equations; Low Mach number

Indexed keywords

ACOUSTIC WAVE VELOCITY; ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; COMPRESSIBLE FLOW; EQUATIONS OF STATE; FLUIDS; LAGRANGE MULTIPLIERS; LINEAR EQUATIONS; MATHEMATICAL MODELS; THEOREM PROVING;

EID: 1642421833     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139902400738     Document Type: Article
Times cited : (9)

References (35)
  • 1
    • 0012281253 scopus 로고
    • On the incompressible limit of the compressible Euler equation
    • K. Asano, On the incompressible limit of the compressible Euler equation, Japan J. Appl. Math., 4 (1987), pp. 455-488.
    • (1987) Japan J. Appl. Math. , vol.4 , pp. 455-488
    • Asano, K.1
  • 2
    • 0040159978 scopus 로고    scopus 로고
    • The modulation equations of nonlinear geometric optics
    • C. Cheverry, The modulation equations of nonlinear geometric optics, Comm. Partial Differential Equations, 21 (1996), pp. 1119-1140.
    • (1996) Comm. Partial Differential Equations , vol.21 , pp. 1119-1140
    • Cheverry, C.1
  • 3
    • 0002084786 scopus 로고    scopus 로고
    • Justification de l'optique geometrique non lineaire pour un systeme de lois de conservation
    • C. Cheverry, Justification de l'optique geometrique non lineaire pour un systeme de lois de conservation, Duke Math. J., 87 (1997), pp. 213-263.
    • (1997) Duke Math. J. , vol.87 , pp. 213-263
    • Cheverry, C.1
  • 4
    • 34250110146 scopus 로고
    • The validity of nonlinear geometric optics for weak solutions of conservation laws
    • R. DiPerna and A. Majda, The validity of nonlinear geometric optics for weak solutions of conservation laws, Comm. Math. Phys., 98 (1985), pp. 313-347.
    • (1985) Comm. Math. Phys. , vol.98 , pp. 313-347
    • DiPerna, R.1    Majda, A.2
  • 5
    • 0022917172 scopus 로고
    • Resonantly interacting weakly nonlinear hyperbolic waves II. Several space variables
    • J. K. Hunter, A. Majda, and R. R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves II. Several space variables, Stud. Appl. Math., 75 (1986), pp. 187-226.
    • (1986) Stud. Appl. Math. , vol.75 , pp. 187-226
    • Hunter, J.K.1    Majda, A.2    Rosales, R.R.3
  • 6
    • 84990566608 scopus 로고
    • Weakly nonlinear high frequency waves
    • J. K. Hunter and J. B. Keller, Weakly nonlinear high frequency waves, Comm. Pure Appl. Math., 36 (1983), pp. 547-569.
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 547-569
    • Hunter, J.K.1    Keller, J.B.2
  • 8
    • 0012275850 scopus 로고
    • Singular limits for the compressible Euler equation in an exterior domain
    • H. Isozaki, Singular limits for the compressible Euler equation in an exterior domain, J. Reine Angew. Math., 381 (1987), pp. 1-36.
    • (1987) J. Reine Angew. Math. , vol.381 , pp. 1-36
    • Isozaki, H.1
  • 9
    • 84972561191 scopus 로고
    • Singular limits for the compressible Euler equation in an exterior domain. II. Bodies in a uniform flow
    • H. Isozaki, Singular limits for the compressible Euler equation in an exterior domain. II. Bodies in a uniform flow, Osaka J. Math., 26 (1989), pp. 399-410.
    • (1989) Osaka J. Math. , vol.26 , pp. 399-410
    • Isozaki, H.1
  • 10
    • 0001198693 scopus 로고
    • Resonant one-dimensional nonlinear geometric optics
    • J. L. Joly, G. Métiver, and J. Rauch, Resonant one-dimensional nonlinear geometric optics, J. Funct. Anal., 114 (1993), pp. 106-231.
    • (1993) J. Funct. Anal. , vol.114 , pp. 106-231
    • Joly, J.L.1    Métiver, G.2    Rauch, J.3
  • 11
    • 0002985997 scopus 로고
    • Coherent and focusing multidimensional nonlinear geometric optics
    • J. L. Joly, G. Métivier, and J. Rauch, Coherent and focusing multidimensional nonlinear geometric optics, Ann. Sci. École Norm. Sup. (4), 28 (1995), pp. 51-113.
    • (1995) Ann. Sci. École Norm. Sup. , vol.28 , Issue.4 , pp. 51-113
    • Joly, J.L.1    Métivier, G.2    Rauch, J.3
  • 12
    • 84974000680 scopus 로고
    • Nonlinear resonance can create dense oscillations
    • M. Beals, R. Melrose, and J. Rauch, eds., Springer-Verlag, New York
    • J. L. Joly and J. Rauch, Nonlinear resonance can create dense oscillations, in Microlocal Analysis and Nonlinear Waves, IMA Vol. Math. Appl. 30, M. Beals, R. Melrose, and J. Rauch, eds., Springer-Verlag, New York, 1991, pp. 113-123.
    • (1991) Microlocal Analysis and Nonlinear Waves, IMA Vol. Math. Appl. , vol.30 , pp. 113-123
    • Joly, J.L.1    Rauch, J.2
  • 13
    • 84980156074 scopus 로고
    • Singular perturbation of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
    • S. Klainerman and A. Majda, Singular perturbation of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math., 34 (1981), pp. 481-524.
    • (1981) Comm. Pure Appl. Math. , vol.34 , pp. 481-524
    • Klainerman, S.1    Majda, A.2
  • 14
    • 84990557419 scopus 로고
    • Compressible and incompressible fluids
    • S. Klainerman and A. Majda, Compressible and incompressible fluids, Comm. Pure Appl. Math., 35 (1982), pp. 629-651.
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 629-651
    • Klainerman, S.1    Majda, A.2
  • 15
    • 0000578716 scopus 로고
    • Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics I: One-dimensional flow
    • R. Klein, Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics I: One-dimensional flow, J. Comput. Phys., 121 (1995), pp. 213-237.
    • (1995) J. Comput. Phys. , vol.121 , pp. 213-237
    • Klein, R.1
  • 17
    • 0023960658 scopus 로고
    • Cumulative effects of weak pressure waves during the induction period of a thermal explosion in a closed cylinder
    • R. Klein and N. Peters, Cumulative effects of weak pressure waves during the induction period of a thermal explosion in a closed cylinder, J. Fluid Mech., 187 (1988), pp. 197-230.
    • (1988) J. Fluid Mech. , vol.187 , pp. 197-230
    • Klein, R.1    Peters, N.2
  • 19
    • 0041082001 scopus 로고
    • Nonlinear geometric optics for hyperbolic systems of conservation laws
    • C. Dafermos, J. Erikson, D. Kinderlehrer, and M. Slemrod, eds., Springer-Verlag, New York
    • A. Majda, Nonlinear geometric optics for hyperbolic systems of conservation laws, in Oscillation Theory, Computation and Methods of Compensated Compactness, IMA Vol. Math. Appl. 2, C. Dafermos, J. Erikson, D. Kinderlehrer, and M. Slemrod, eds., Springer-Verlag, New York, 1986, pp. 115-165.
    • (1986) Oscillation Theory, Computation and Methods of Compensated Compactness, IMA Vol. Math. Appl. 2 , pp. 115-165
    • Majda, A.1
  • 20
    • 0021502758 scopus 로고
    • Resonantly interacting weakly nonlinear hyperbolic waves I. A single space variable
    • A. Majda and R. R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves I. A single space variable, Stud. Appl. Math., 71 (1983), pp. 149.
    • (1983) Stud. Appl. Math. , vol.71 , pp. 149
    • Majda, A.1    Rosales, R.R.2
  • 21
    • 84948505075 scopus 로고
    • The derivation and numerical solution of the equations for zero Mach number combustion
    • A. Majda and J. Sethian, The derivation and numerical solution of the equations for zero Mach number combustion, Combustion Science and Technology, 42 (1985), pp. 185-205.
    • (1985) Combustion Science and Technology , vol.42 , pp. 185-205
    • Majda, A.1    Sethian, J.2
  • 22
    • 0007109251 scopus 로고
    • Nearly incompressible magnetohydrodynamics at low Mach number
    • W. H. Matthaeus and M. R. Brown, Nearly incompressible magnetohydrodynamics at low Mach number, Phys. Fluids, 31 (1988), pp. 3634-3644.
    • (1988) Phys. Fluids , vol.31 , pp. 3634-3644
    • Matthaeus, W.H.1    Brown, M.R.2
  • 23
    • 0343193151 scopus 로고    scopus 로고
    • Asymptotic single and multiple scale expansions in the low Mach number limit
    • A. Meister, Asymptotic single and multiple scale expansions in the low Mach number limit, SIAM J. Appl. Math., 60 (1999), pp. 256-271.
    • (1999) SIAM J. Appl. Math. , vol.60 , pp. 256-271
    • Meister, A.1
  • 24
    • 35949012093 scopus 로고
    • Riemann problem for fluid flow of real materials
    • R. Menikoff and B. J. Plohr, Riemann problem for fluid flow of real materials, Rev. Modern Phys., 61 (1989), pp. 75-130.
    • (1989) Rev. Modern Phys. , vol.61 , pp. 75-130
    • Menikoff, R.1    Plohr, B.J.2
  • 25
    • 0035644949 scopus 로고    scopus 로고
    • The incompressible limit of the non-isentropic Euler equations
    • G. Métivier and S. Schochet, The incompressible limit of the non-isentropic Euler equations, Arch. Ration. Mech. Anal., 158 (2001), pp. 61-90.
    • (2001) Arch. Ration. Mech. Anal. , vol.158 , pp. 61-90
    • Métivier, G.1    Schochet, S.2
  • 26
    • 0039830700 scopus 로고
    • Some explicit resonating waves in weakly nonlinear gas dynamics
    • R. Pego, Some explicit resonating waves in weakly nonlinear gas dynamics, Stud. Appl. Math., 79 (1988), pp. 263-270.
    • (1988) Stud. Appl. Math. , vol.79 , pp. 263-270
    • Pego, R.1
  • 27
    • 0002442528 scopus 로고
    • The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit
    • S. Schochet, The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit, Comm. Math. Phys., 104 (1986), pp. 49-75.
    • (1986) Comm. Math. Phys. , vol.104 , pp. 49-75
    • Schochet, S.1
  • 28
    • 0005500852 scopus 로고
    • Resonant nonlinear geometric optics for weak solutions of conservation laws
    • S. Schochet, Resonant nonlinear geometric optics for weak solutions of conservation laws, J. Differential Equations, 113 (1994), pp. 473-504.
    • (1994) J. Differential Equations , vol.113 , pp. 473-504
    • Schochet, S.1
  • 29
    • 43949155251 scopus 로고
    • Fast singular limits of hyperbolic PDEs
    • S. Schochet, Fast singular limits of hyperbolic PDEs, J. Differential Equations, 114 (1994), pp. 476-512.
    • (1994) J. Differential Equations , vol.114 , pp. 476-512
    • Schochet, S.1
  • 31
    • 0000880485 scopus 로고    scopus 로고
    • Extension of finite volume compressible flow solvers to multi-dimensional, variable density, zero Mach number flow
    • Th. Schneider, N. Botta, K.-J. Geratz, and R. Klein, Extension of finite volume compressible flow solvers to multi-dimensional, variable density, zero Mach number flow, J. Comput. Phys., 155 (1999), pp. 248-286.
    • (1999) J. Comput. Phys. , vol.155 , pp. 248-286
    • Schneider, Th.1    Botta, N.2    Geratz, K.-J.3    Klein, R.4
  • 32
    • 24444448464 scopus 로고    scopus 로고
    • Simulazione numerica della compressione di un pistone e confronto con l'approssimazione adiabatica
    • Tesi di laurea, Università dell'Aquila, L'Aquila, Italy
    • F. Tiberi Timperi, Simulazione numerica della compressione di un pistone e confronto con l'approssimazione adiabatica, Tesi di laurea, Università dell'Aquila, L'Aquila, Italy. 1997.
    • (1997)
    • Tiberi Timperi, F.1
  • 33
    • 0000570341 scopus 로고
    • The incompressible limit and the initial layer of the compressible Euler equation
    • S. Ukai, The incompressible limit and the initial layer of the compressible Euler equation, J. Math. Kyoto Univ., 26 (1986), pp. 323-331.
    • (1986) J. Math. Kyoto Univ. , vol.26 , pp. 323-331
    • Ukai, S.1
  • 34
    • 0026004239 scopus 로고
    • The equations of nearly incompressible fluids. I. Hydrodynamics, turbulence and waves
    • G. P. Zank and W. H. Matthaeus, The equations of nearly incompressible fluids. I. Hydrodynamics, turbulence and waves, Phys. Fluids A, 3 (1991), pp. 69-82.
    • (1991) Phys. Fluids A , vol.3 , pp. 69-82
    • Zank, G.P.1    Matthaeus, W.H.2
  • 35
    • 0027492712 scopus 로고
    • Nearly incompressible fluids. II. Magnetohydrodynamics, turbulence and waves
    • G. P. Zank and W. H. Matthaeus, Nearly incompressible fluids. II. Magnetohydrodynamics, turbulence and waves, Phys. Fluids A, 5 (1993), pp. 257-273.
    • (1993) Phys. Fluids A , vol.5 , pp. 257-273
    • Zank, G.P.1    Matthaeus, W.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.