满足3个守恒律的Godunov型格式
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摘要
为将已有的一维守恒律方程满足多个守恒律的Godunov型格式推广到高维守恒律方程中,对二维的线性传输方程设计了一个满足3个守恒律的Godunov型格式.数值试验表明,该格式具有长时间的保结构性.
In order to apply Godunov type scheme satisfying several conservation laws for one dimensional hyperbolic conservation laws to multi-dimensional hyperbolic conservation laws,this paper designs a Godunov type scheme satisfying three conservation laws for two dimensional linear advection equation.The numerical experiments show that this scheme has good structure preserving property in long time numerical simulations.
In order to apply Godunov type scheme satisfying several conservation laws for one dimensional hyperbolic conservation laws to multi-dimensional hyperbolic conservation laws,this paper designs a Godunov type scheme satisfying three conservation laws for two dimensional linear advection equation.The numerical experiments show that this scheme has good structure preserving property in long time numerical simulations.
引文
[1]Harten A.High resolution schemes for hyperbolic conservation laws[J].Journal of Computational Physics,1983,49(3):357-393.
[2]SHU Chi-wang.TVB uniformly high-order schemes for conservation laws[J].Mathmatics of Computa-tion,1987,49(179):105-121.
[3]Harten A,Osher S.Uniformly high-order accurate nonoscillatory scheme I[J].SIAM Journal on Numer-ical Analysis,1987,24(2):279-309.
[4]Harten A,Engquist B,Osher S,et al.Uniformly high order accurate essentially non-oscillatory scheme III[J].Journal of Computational Physics,1987,71(2):231-303.
[5]SHU Chi-wang,Osher S.Efficient implementation of essentially non-oscillatory shock capturing schemes[J].Journal of Computational Physics,1988,77(2):439-471.
[6]Colella P,Woodward P.The piecewise parabolic method(PPM)for gas-dynamical simulations[J].Journal of Computational Physics,1984,54(1):174-201.
[7]Colella P.Multidimensional upwind methods for hy-perbolic conservation laws[J].Journal of Computa-tional Physics,1990,87(1):171-200.
[8]JIANG Guang-shan,SHU Chi-wang.Efficient im-plementation of weighted ENO schemes[J].Journal of Computational Physics,1996,22:202-228.
[9]李红霞,茅德康.单个守恒律方程的熵耗散格式中耗散函数的构造[J].计算物理,2004,21(3):319-326.LI Hong-xia,MAO De-kang.The design of the en-tropy dissipator of the entropy dissipating scheme for scalar conservation law[J].Chinese Journal of Com-putational Physics,2004,21(3):319-326.
[10]王志刚,茅德康.线性传输方程满足3个守恒律的差分格式[J].上海大学学报,2006,12(6):588-592.WANG Zhi-gang,MAO De-kang.Conservative difference scheme satisfying three conservation laws for linear advection equation[J].Journal of Shanghai University,2006,12(6):588-592,
[11]LI Hong-xia,WANG Zhi-gang,MAO De-kang.Nu-merically neither dissipative nor compressive scheme for linear advection equation and its application to the Euler system[J].Journal of Scientific Computing,2008,36(3):285-331.
[12]CUI Yan-fen,MAO De-kang.Numerical method sat-isfying the first two conservation laws for the Korte-weg-de Vries equation[J].Journal of Computational Physics,2007,227(1):376-399.
[13]CUI Yan-fen,MAO De-kang.Error self-canceling of a difference scheme maintaining two conservation laws for linear advection equation[J].Mathmatics of Computation,2012,81(278):715-741.
[14]Leveque R J.Finite volume methods for hyperbolic problem[M].Cambridge:Cambridge University Press,2002:64-85.
[2]SHU Chi-wang.TVB uniformly high-order schemes for conservation laws[J].Mathmatics of Computa-tion,1987,49(179):105-121.
[3]Harten A,Osher S.Uniformly high-order accurate nonoscillatory scheme I[J].SIAM Journal on Numer-ical Analysis,1987,24(2):279-309.
[4]Harten A,Engquist B,Osher S,et al.Uniformly high order accurate essentially non-oscillatory scheme III[J].Journal of Computational Physics,1987,71(2):231-303.
[5]SHU Chi-wang,Osher S.Efficient implementation of essentially non-oscillatory shock capturing schemes[J].Journal of Computational Physics,1988,77(2):439-471.
[6]Colella P,Woodward P.The piecewise parabolic method(PPM)for gas-dynamical simulations[J].Journal of Computational Physics,1984,54(1):174-201.
[7]Colella P.Multidimensional upwind methods for hy-perbolic conservation laws[J].Journal of Computa-tional Physics,1990,87(1):171-200.
[8]JIANG Guang-shan,SHU Chi-wang.Efficient im-plementation of weighted ENO schemes[J].Journal of Computational Physics,1996,22:202-228.
[9]李红霞,茅德康.单个守恒律方程的熵耗散格式中耗散函数的构造[J].计算物理,2004,21(3):319-326.LI Hong-xia,MAO De-kang.The design of the en-tropy dissipator of the entropy dissipating scheme for scalar conservation law[J].Chinese Journal of Com-putational Physics,2004,21(3):319-326.
[10]王志刚,茅德康.线性传输方程满足3个守恒律的差分格式[J].上海大学学报,2006,12(6):588-592.WANG Zhi-gang,MAO De-kang.Conservative difference scheme satisfying three conservation laws for linear advection equation[J].Journal of Shanghai University,2006,12(6):588-592,
[11]LI Hong-xia,WANG Zhi-gang,MAO De-kang.Nu-merically neither dissipative nor compressive scheme for linear advection equation and its application to the Euler system[J].Journal of Scientific Computing,2008,36(3):285-331.
[12]CUI Yan-fen,MAO De-kang.Numerical method sat-isfying the first two conservation laws for the Korte-weg-de Vries equation[J].Journal of Computational Physics,2007,227(1):376-399.
[13]CUI Yan-fen,MAO De-kang.Error self-canceling of a difference scheme maintaining two conservation laws for linear advection equation[J].Mathmatics of Computation,2012,81(278):715-741.
[14]Leveque R J.Finite volume methods for hyperbolic problem[M].Cambridge:Cambridge University Press,2002:64-85.