On the relaxation approximation of boundary control of the isothermal Euler equations
On the relaxation approximation of boundary control of the isothermal Euler equations
复制标题
等温欧拉方程边界控制的松弛近似
DOI：
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复制
发表时间：
2012
影响因子：
2.1
通讯作者：
S. Steffensen
中科院分区：
文献类型：
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作者：
Markus Hirsch;M. Gugat;M. Herty;S. Steffensen
我们考虑无摩擦的等温欧拉方程来模拟气体在管道中的流动。我们考虑了该系统在给定定态附近的局部边界稳定问题。我们提出了一个反馈律，它在物理变量上是线性的，并产生了系统状态的指数衰减。对于具有守恒律的双曲型系统的数值解，可以采用Jin-Xin松弛格式。因此，我们也考虑了线性黎曼反馈松弛系统的边界稳定性，并给出了稳定系统的快速指数衰减的数值例子。
We consider the isothermal Euler equations without friction that simulate gas flow through a pipe. We consider the problem of boundary stabilisation of this system locally around a given stationary state. We present a feedback law that is linear in the physical variables and yields exponential decay of the system state. For the numerical solution of hyperbolic systems of conservation laws, the Jin–Xin relaxation scheme can be used. Therefore, we also consider the boundary stabilisation of the relaxation system by the linear Riemann feedback and present numerical examples that show the rapid exponential decay of the stabilised system.