线性传输方程的Entropy-Monotone格式
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摘要
在守恒律方程组的数值计算中,线性间断的磨损问题备受关注.为了减少线性间断的磨损,针对线性传输方程,提出了Entropy-Monotone格式.该格式属于Godunov型格式,包括重构、发展和求网格平均3个步骤.与传统的Godunov格式不同,该格式同时计算数值解和数值熵,并通过它们构造分片常数的台阶函数.数值实验表明,此格式对线性间断的模拟非常有效.
In numerical computation of conservation laws,the problem of the wear of linear discontinuity is of great concern.In order to decrease the wear of linear discontinuity,an entropy-monotone scheme was designed for the linear advection equation.This scheme is a Godunov scheme,which includes reconstruction,evolution,and cell-averaging.Different from the traditional Godunov scheme,this scheme simultaneously computes the numerical solution and numerical entropy,and uses them to reconstruction the"step function"in each cell.Numerical experiments show that this scheme is very effective for the simulation of linear discontinuity.
In numerical computation of conservation laws,the problem of the wear of linear discontinuity is of great concern.In order to decrease the wear of linear discontinuity,an entropy-monotone scheme was designed for the linear advection equation.This scheme is a Godunov scheme,which includes reconstruction,evolution,and cell-averaging.Different from the traditional Godunov scheme,this scheme simultaneously computes the numerical solution and numerical entropy,and uses them to reconstruction the"step function"in each cell.Numerical experiments show that this scheme is very effective for the simulation of linear discontinuity.
引文
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[6]JIANG Guangshan,SHU Chiwang.Efficient implementation of weighted ENO schemes[J].Journal of Computational Physics,1996,126(1):202-228.
[7]COLELLA P,WOODWARD P R.The piecewise parabolic method(PPM)for gas-dynamical simulations[J].Journal of Computational Physics,1984,54(1):174-201.
[8]COLELLA P.Multidimensional upwind methods for hyperbolic conservation laws[J].Journal of Computational Physics,1990,87(1):171-200.
[9]LI Hongxia,WANG Zhigang,MAO Dekang.Numerically 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.
[10]CHEN Rongsan,MAO Dekang.Entropy-TVD scheme for nonlinear scalar conservation laws[J].Journal of Scientific Computing,2011,47(2):150-169.
[11]Lagoutière F.Stability of reconstruction schemes for scalar hyperbolic conservations laws[J].Communications in Mathematical Sciences,2008,6(1):57-70.
[12]Leveque R J.Finite volume methods for hyperbolic problem[M].Cambridge:Cambridge University Press,2002:64-85.
[2]SHU Chiwang.TVB uniformly high-order schemes for conservation laws[J].Mathmatics Computation,1987,49(179):105-121.
[3]HARTEN A,OSHER S.Uniformly high-order accurate nonoscillatory schemeⅠ[J].SIAM Journal on Numerical Analysis,1987,24(2):279-309.
[4]HARTEN A,ENGQUIST B,OSHER S,et al.Uniformly high order accurate essentially non-oscillatory schemeⅢ[J].Journal of Computational Physics,1986,71(2):231-303.
[5]SHU Chiwang,OSHER S.Efficient implementation of essentially non-oscillatory shock capturing schemes[J].Journal of Computational Physics,1988,77(2):439-471.
[6]JIANG Guangshan,SHU Chiwang.Efficient implementation of weighted ENO schemes[J].Journal of Computational Physics,1996,126(1):202-228.
[7]COLELLA P,WOODWARD P R.The piecewise parabolic method(PPM)for gas-dynamical simulations[J].Journal of Computational Physics,1984,54(1):174-201.
[8]COLELLA P.Multidimensional upwind methods for hyperbolic conservation laws[J].Journal of Computational Physics,1990,87(1):171-200.
[9]LI Hongxia,WANG Zhigang,MAO Dekang.Numerically 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.
[10]CHEN Rongsan,MAO Dekang.Entropy-TVD scheme for nonlinear scalar conservation laws[J].Journal of Scientific Computing,2011,47(2):150-169.
[11]Lagoutière F.Stability of reconstruction schemes for scalar hyperbolic conservations laws[J].Communications in Mathematical Sciences,2008,6(1):57-70.
[12]Leveque R J.Finite volume methods for hyperbolic problem[M].Cambridge:Cambridge University Press,2002:64-85.