变截面管道磁气体动力学守恒律方程组的基本波（英文）
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摘要
根据质量守恒定律、动量守恒定律以及能量守恒定律推导了变截面管道等熵磁气体动力学守恒律方程组.利用特征分析法给出了基本波曲线表达式.引入全局熵条件唯一确定驻波解,并证明了驻波的一些性质.
The equations of conservation laws in isentropic magnetogasdynamics in a variable cross-section duct are deducted by the law of conservation of mass,the law of conservation of momentum, and the law of conservation of energy. We present the expressions of elementary waves relying on the characteristic analysis method. The uniqueness of the stationary solution can be determined by imposing a global entropy condition and some properties of stationary waves are proved.
The equations of conservation laws in isentropic magnetogasdynamics in a variable cross-section duct are deducted by the law of conservation of mass,the law of conservation of momentum, and the law of conservation of energy. We present the expressions of elementary waves relying on the characteristic analysis method. The uniqueness of the stationary solution can be determined by imposing a global entropy condition and some properties of stationary waves are proved.
引文
[1] Li D Q, Qin T H. Physics and Partial Differential Equations[M]. Beijing:High Education Press, 2005.(in Chinese)
[2] Hu W R. Universe Magnetogas dynamics[M]. Beijing:Science Press, 1989.(in Chinese)
[3] Sekhar T R, Sharma V D. Riemann problem and elementary wave interactions in isentropic magnetogasdynamics[J]. Nolinear Analysis:Real World Applications, 2010, 11:619-636.
[4] Hu Y B, Sheng W C. The Riemann problem of conservation laws in magnetogasdynamics[J].Communications on Pure and Applied Analysis, 2013, 12:755-769.
[5] Isaacson E, Temple B. Nonlinear resonance in systems of conservation laws[J]. SIAM Journal on Applied Mathematics, 1992, 52:1260-1278.
[6] LeFloch P G, Thanh M D. The Riemann problem for fluid flows in a nozzle with discontinuous cross-section[J]. Commun Math Sci, 2003, 1:763-797.
[7] Thanh M D. The Riemann problem for a nonisentropic fluid in a nozzle with discontinuous cross-sectional area[J]. SIAM Journal on Applied Mathematics, 2009, 69:1501-1519.
[8] Sheng W C, Zhang Q L. The interaction of the elementary waves of isentropic flow in a variable cross-section duct[J]. Commun Appl Math Comput, 2018, 32(2):374-382.
[2] Hu W R. Universe Magnetogas dynamics[M]. Beijing:Science Press, 1989.(in Chinese)
[3] Sekhar T R, Sharma V D. Riemann problem and elementary wave interactions in isentropic magnetogasdynamics[J]. Nolinear Analysis:Real World Applications, 2010, 11:619-636.
[4] Hu Y B, Sheng W C. The Riemann problem of conservation laws in magnetogasdynamics[J].Communications on Pure and Applied Analysis, 2013, 12:755-769.
[5] Isaacson E, Temple B. Nonlinear resonance in systems of conservation laws[J]. SIAM Journal on Applied Mathematics, 1992, 52:1260-1278.
[6] LeFloch P G, Thanh M D. The Riemann problem for fluid flows in a nozzle with discontinuous cross-section[J]. Commun Math Sci, 2003, 1:763-797.
[7] Thanh M D. The Riemann problem for a nonisentropic fluid in a nozzle with discontinuous cross-sectional area[J]. SIAM Journal on Applied Mathematics, 2009, 69:1501-1519.
[8] Sheng W C, Zhang Q L. The interaction of the elementary waves of isentropic flow in a variable cross-section duct[J]. Commun Appl Math Comput, 2018, 32(2):374-382.