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学者姓名：邵志强
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Abstract ：
We study the piston problem for the compressible fluid flow of generalized Chaplygin gas, for both cases that the piston rushes into or recedes from the uniform still gas at a constant speed. The global existence of a solution to the piston problem is established. For the proceeding piston problem, we find that the front shock can be detached or adhered to the surface of the piston depending on the range of Mach numbers. Then, a Radon measure solution, with density containing a Dirac measure supported on the piston is rigorously defined and proved to be a reasonable solution to deal with the concentration of mass on the piston. When the piston recedes from the gas, we show strictly that only a first -family rarefaction wave exists in front of the piston and that concentration will never occur. Moreover, we also analyzed the occurrence of the vacuum state and the degeneration of the compressible fluid flow in the receding case as the Mach number tends to infinity.
Keyword ：
Compressible fluid flow Compressible fluid flow Generalized Chaplygin gas Generalized Chaplygin gas Measure solution Measure solution Piston problem Piston problem
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| GB/T 7714 | Huang, Meixiang , Wang, Yuanjin , Shao, Zhiqiang . Piston problem for the generalized Chaplygin Euler equations of compressible fluid flow [J]. | CHINESE JOURNAL OF PHYSICS , 2024 , 89 : 810-819 . |
| MLA | Huang, Meixiang 等. "Piston problem for the generalized Chaplygin Euler equations of compressible fluid flow" . | CHINESE JOURNAL OF PHYSICS 89 (2024) : 810-819 . |
| APA | Huang, Meixiang , Wang, Yuanjin , Shao, Zhiqiang . Piston problem for the generalized Chaplygin Euler equations of compressible fluid flow . | CHINESE JOURNAL OF PHYSICS , 2024 , 89 , 810-819 . |
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Abstract ：
In this paper, we investigate the concentration and cavitation phenomena of Riemann solutions for the generalized Chaplygin gas equations in the presence of flux approximation. The concentration and cavitation are fundamental and physical phenomena in fluid dynamics, which can be mathematically described by delta shock waves and vacuums (or constant density states), respectively. The main objective of this paper is to rigorously investigate the formation of delta shock waves and constant density states and observe the concentration and cavitation phenomena. First, the Riemann problem for the generalized Chaplygin gas equations under the flux approximation is solved constructively. Although the system is strictly hyperbolic and its two characteristic fields are genuinely nonlinear, the delta shock wave arises in Riemann solutions. The formation of mechanism for delta shock wave is analyzed, that is, the 1-shock wave curve and the 2-shock wave curve do not intersect each other in the phase plane. Second, it is rigorously proved that, as the pressure vanishes, the Riemann solutions for the generalized Chaplygin gas equations under the flux approximation tend to the two kinds of Riemann solutions to the transport equations in zero-pressure flow under the flux approximation, which include a delta shock wave formed by a weighted δ-measure and a constant density state. © 2024 Author(s).
Keyword ：
Cavitation Cavitation Gas dynamics Gas dynamics Shock waves Shock waves
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| GB/T 7714 | Shao, Zhiqiang , Huang, Meixiang . Concentration and cavitation phenomena of Riemann solutions for the generalized Chaplygin gas equations under the flux approximation [J]. | Physics of Fluids , 2024 , 36 (7) . |
| MLA | Shao, Zhiqiang 等. "Concentration and cavitation phenomena of Riemann solutions for the generalized Chaplygin gas equations under the flux approximation" . | Physics of Fluids 36 . 7 (2024) . |
| APA | Shao, Zhiqiang , Huang, Meixiang . Concentration and cavitation phenomena of Riemann solutions for the generalized Chaplygin gas equations under the flux approximation . | Physics of Fluids , 2024 , 36 (7) . |
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In this paper, we study the Riemann problem with the initial data containing the Dirac delta function in both components for a nonstrictly hyperbolic system of two conservation laws from zero-pressure gas dynamics by introducing the new state variabe. In solutions, we find another kind of delta shocks on which both state variables simultaneously contain the Dirac delta functions. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. This phenomenon is also captured numerically and experimentally by Kreji, Kruni and Nedeljkov [N. Kreji, T. Kruni, M. Nedeljkov, Numerical verification of delta shock waves for pressureless gas dynamics, J. Math. Anal. Appl. 345 (2008) 243-257]. Moreover, a new kind of nonclassical wave, namely a delta contact discontinuity, is discovered here, which is a Dirac delta function supported on a contact discontinuity.
Keyword ：
Delta shock wave Delta shock wave Generalized Rankine-Hugoniot relation Generalized Rankine-Hugoniot relation Generalized solution Generalized solution Pressureless gas dynamic model Pressureless gas dynamic model Riemann problem Riemann problem Vacuum state Vacuum state
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| GB/T 7714 | Shao, Zhiqiang . The Riemann problem with delta initial data with Dirac delta function in both components for a pressureless gas dynamic model [J]. | INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS , 2024 . |
| MLA | Shao, Zhiqiang . "The Riemann problem with delta initial data with Dirac delta function in both components for a pressureless gas dynamic model" . | INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS (2024) . |
| APA | Shao, Zhiqiang . The Riemann problem with delta initial data with Dirac delta function in both components for a pressureless gas dynamic model . | INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS , 2024 . |
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In this paper, we investigate the limiting behavior of Riemann solutions to the Euler equations of compressible fluid flow for modified Chaplygin gas with the body force as the two parameters tend to zero. The formation of delta shock waves and the vacuum states is identified and analyzed during the process of vanishing pressure in the Riemann solutions. The concentration and cavitation are fundamental and physical phenomena in fluid dynamics, which can be mathematically described by delta shock waves and vacuums, respectively. In this paper, our main objective is to rigorously investigate the formation of delta shock waves and vacuums and observe the concentration and cavitation phenomena. First, the Riemann problem of the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force is solved. Second, we rigorously confirm that, as the pressure vanishes, any two shock Riemann solution to the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force tends to a delta-shock solution to the pressureless gas dynamics model with a body force, and the intermediate density between the two shocks tends to a weighted delta-measure that forms the delta-shock; any two-rarefaction-wave Riemann solution to the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force tends to a solution consisting of four contact discontinuities together with vacuum states with three different virtual velocities in the limiting situation.
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| GB/T 7714 | Zhu, Jiayi , Huang, Meixiang , Shao, Zhiqiang . The limiting behavior of Riemann solutions to the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force [J]. | PHYSICS OF FLUIDS , 2024 , 36 (2) . |
| MLA | Zhu, Jiayi 等. "The limiting behavior of Riemann solutions to the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force" . | PHYSICS OF FLUIDS 36 . 2 (2024) . |
| APA | Zhu, Jiayi , Huang, Meixiang , Shao, Zhiqiang . The limiting behavior of Riemann solutions to the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force . | PHYSICS OF FLUIDS , 2024 , 36 (2) . |
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We constructively solve the piston problem for the one-dimensional isentropic Euler equations for a modified Chaplygin gas. We give a rigorous proof of the global existence and uniqueness of a shock wave separating constant states ahead of the piston when the piston advances into the gas. The results are quite different from those for a pure Chaplygin gas or a generalized Chaplygin gas, in which a Radon measure solution is constructed to deal with the concentration of mass on the piston. When the piston recedes from the gas, we show strictly that only a first-family rarefaction wave exists in front of the piston and that concentration will never occur. In addition, by studying the limiting behavior, we show that the piston solutions of the modified Chaplygin gas equations tend to the piston solutions of the generalized or pure Chaplygin gas equations as a single parameter of the pressure state function vanishes.
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| GB/T 7714 | Huang, Meixiang , Wang, Yuanjin , Shao, Zhiqiang . Piston problem for the isentropic Euler equations for a modified Chaplygin gas [J]. | PHYSICS OF FLUIDS , 2023 , 35 (1) . |
| MLA | Huang, Meixiang 等. "Piston problem for the isentropic Euler equations for a modified Chaplygin gas" . | PHYSICS OF FLUIDS 35 . 1 (2023) . |
| APA | Huang, Meixiang , Wang, Yuanjin , Shao, Zhiqiang . Piston problem for the isentropic Euler equations for a modified Chaplygin gas . | PHYSICS OF FLUIDS , 2023 , 35 (1) . |
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A traffic flow model describing the formation and dynamics of traffic jams was introduced by Berthelin et al. [ "A model for the formation and evolution of traffic jams, " Arch. Ration. Mech. Anal. 187, 185-220 (2008)], which consists of a pressureless gas dynamics system under a maximal constraint on the density and can be derived from the Aw-Rascle model under the constraint condition rho <= rho* by letting the traffic pressure vanish. In this paper, we give up this constraint condition and consider the following form:{ rho(t) + (rho u)(x) = 0 , (rho u + epsilon p (rho))(t) + (rho u(2) + epsilon up(rho))(x) = 0 , in which p(rho) = - 1/rho. The Riemann problem for the above traffic flow model is constructively solved. The delta shock wave arises in the Riemann solutions, although the system is strictly hyperbolic, its first eigenvalue is genuinely nonlinear, and the second eigenvalue is linearly degenerate. Furthermore, we clarify the generalized Rankine-Hugoniot relations and delta-entropy condition. The position, strength, and propagation speed of the delta shock wave are obtained from the generalized Rankine-Hugoniot conditions. The delta shock may be useful for the description of the serious traffic jam. More importantly, it is proved that the limits of the Riemann solutions of the above traffic flow model are exactly those of the pressureless gas dynamics system with the same Riemann initial data as the traffic pressure vanishes.
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| GB/T 7714 | Shao, Zhiqiang . The Riemann problem for a traffic flow model [J]. | PHYSICS OF FLUIDS , 2023 , 35 (3) . |
| MLA | Shao, Zhiqiang . "The Riemann problem for a traffic flow model" . | PHYSICS OF FLUIDS 35 . 3 (2023) . |
| APA | Shao, Zhiqiang . The Riemann problem for a traffic flow model . | PHYSICS OF FLUIDS , 2023 , 35 (3) . |
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In this paper, we constructively solve the Riemann problem for the relativistic Euler equations with the logarithmic equation of state. The concentration and cavitation phenomena are observed and analyzed during the process of vanishing pressure in the Riemann solutions. It is rigorously proved that, as the pressure vanishes, they tend to the two kinds of Riemann solutions to the zero-pressure relativistic Euler equations, which include a delta shock formed by a weighted d-measure and a vacuum state.
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| GB/T 7714 | Lei, Zhoutong , Shao, Zhiqiang . Concentration and cavitation in the vanishing pressure limit of solutions to the relativistic Euler equations with the logarithmic equation of state [J]. | JOURNAL OF MATHEMATICAL PHYSICS , 2023 , 64 (7) . |
| MLA | Lei, Zhoutong 等. "Concentration and cavitation in the vanishing pressure limit of solutions to the relativistic Euler equations with the logarithmic equation of state" . | JOURNAL OF MATHEMATICAL PHYSICS 64 . 7 (2023) . |
| APA | Lei, Zhoutong , Shao, Zhiqiang . Concentration and cavitation in the vanishing pressure limit of solutions to the relativistic Euler equations with the logarithmic equation of state . | JOURNAL OF MATHEMATICAL PHYSICS , 2023 , 64 (7) . |
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In this paper, we study the occurrence mechanism on the phenomenon of concentration and the formation of delta-shock wave in vanishing adiabatic exponent limit of Riemann solutions to the Aw-Rascle model of traffic flow with a relaxation term. At first, by a special type of variable substitution, the Riemann problems of pressureless gas dynamics and Aw-Rascle model of traffic flow with a relaxation term are solved. Unlike the homogeneous case, both Riemann solutions are no longer self-similar due to the relaxation term. Then, we rigorously prove that, as the adiabatic exponent vanishes, the Riemann solution containing a shock curve and a contact discontinuity of the Aw-Rascle model with a relaxation term tends to a special delta-shock wave, which is different from the delta-shock wave of limiting pressureless gas dynamics model. At last, some numerical simulations are presented to show the formation process of delta-shock waves and illustrate the above analysis.
Keyword ：
Aw-Rascle model Aw-Rascle model Delta-shock wave Delta-shock wave Numerical simulations Numerical simulations Relaxation term Relaxation term Riemann solution Riemann solution
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| GB/T 7714 | Huang, Meixiang , Sheng, Shouqiong , Shao, Zhiqiang . Concentration of mass in the vanishing adiabatic exponent limit of Aw-Rascle traffic model with relaxation [J]. | JOURNAL OF ENGINEERING MATHEMATICS , 2023 , 140 (1) . |
| MLA | Huang, Meixiang 等. "Concentration of mass in the vanishing adiabatic exponent limit of Aw-Rascle traffic model with relaxation" . | JOURNAL OF ENGINEERING MATHEMATICS 140 . 1 (2023) . |
| APA | Huang, Meixiang , Sheng, Shouqiong , Shao, Zhiqiang . Concentration of mass in the vanishing adiabatic exponent limit of Aw-Rascle traffic model with relaxation . | JOURNAL OF ENGINEERING MATHEMATICS , 2023 , 140 (1) . |
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Abstract ：
该文研究带有复合源项的一维可压缩流体欧拉方程组的黎曼问题,其中源项可以是摩擦项,也可以是阻尼项,也可以是阻尼和摩擦两者都具有.与齐次型不同,非齐次守恒律方程组的黎曼解是非自相似的.当绝热指数γ→1即压力消失时,讨论带有复合源项的一维可压缩流体欧拉方程组的黎曼解中集中现象和真空状态的形成,证明包含两条激波的黎曼解收敛于零压下的delta激波解,包含两条稀疏波的黎曼解收敛于零压下的两条接触间断解,其中连接两条接触间断解的中间状态是真空状态.
Keyword ：
Delta激波 Delta激波 可压缩流体欧拉方程组 可压缩流体欧拉方程组 复合源项 复合源项 消失压力极限 消失压力极限 真空状态 真空状态 黎曼问题 黎曼问题
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| GB/T 7714 | 邵志强 . 一维具有阻尼和摩擦项的可压缩流体欧拉方程组当压力消失时黎曼解的极限 [J]. | 数学物理学报 , 2022 , 42 (04) : 1150-1172 . |
| MLA | 邵志强 . "一维具有阻尼和摩擦项的可压缩流体欧拉方程组当压力消失时黎曼解的极限" . | 数学物理学报 42 . 04 (2022) : 1150-1172 . |
| APA | 邵志强 . 一维具有阻尼和摩擦项的可压缩流体欧拉方程组当压力消失时黎曼解的极限 . | 数学物理学报 , 2022 , 42 (04) , 1150-1172 . |
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Abstract ：
In this paper, we study the formation of delta shock waves and vacuum states in a pressureless limit of solutions to the Euler equations of compressible fluid flow for modified Chaplygin gas as two parameters tend to zero. At first, the Riemann problem of Euler equations of compressible fluid flow for modified Chaplygin gas is solved. Then, as the pressure drops to zero, we strictly confirm that the two-shock Riemann solution converges to a delta shock wave solution and the two-rarefaction wave Riemann solution converges to a two-contact discontinuity solution with the intermediate state approaching a vacuum state. At last, some numerical simulations are given to verify the above analysis.
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| GB/T 7714 | Lei, Zhoutong , Shao, Zhiqiang . The limit behavior of Riemann solutions to the Euler equations of compressible fluid flow for the modified Chaplygin gas [J]. | JOURNAL OF MATHEMATICAL PHYSICS , 2022 , 63 (7) . |
| MLA | Lei, Zhoutong 等. "The limit behavior of Riemann solutions to the Euler equations of compressible fluid flow for the modified Chaplygin gas" . | JOURNAL OF MATHEMATICAL PHYSICS 63 . 7 (2022) . |
| APA | Lei, Zhoutong , Shao, Zhiqiang . The limit behavior of Riemann solutions to the Euler equations of compressible fluid flow for the modified Chaplygin gas . | JOURNAL OF MATHEMATICAL PHYSICS , 2022 , 63 (7) . |
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