论文标题
可压缩不混溶的两相动力学的尖锐界面限制与放松
Sharp Interface Limit for Compressible Immiscible Two-Phase Dynamics with Relaxation
论文作者
论文摘要
在本文中，研究了带有松弛的可压缩不混溶的两相流，该模型可以被视为由S.Jin和Z.P.xin提出和开发的Jin-Xin弛豫方案的自然修饰（[[Comm.pure Appl.Math。，48,1995]），鉴于数值的维护法律的数值近似法。 Given any entropy solution consists of two different families of shocks interacting at some positive time for the standard two-phase compressible Euler equations, it is proved that such entropy solution is the sharp interface limit for a family global strong solutions of the modified Jin-Xin relaxation scheme for Navier-Stokes/Allen-Cahn system, here the relaxation time is selected as the thickness of the interface, weighted estimation and improved antiderivative method are used in the proof.此外，模拟结果由这种修改后的Jin-Xin弛豫方案方法给出。数值和理论结果都表明，相互作用的冲击波可以通过界面而不会产生任何影响。
In this paper, the compressible immiscible two-phase flow with relaxation is investigated, this model can be regarded as a natural modification of Jin-Xin relaxation scheme proposed and developed by S.Jin and Z.P.Xin([Comm.Pure Appl.Math., 48,1995]) in view of the numerical approximation of conservation laws. Given any entropy solution consists of two different families of shocks interacting at some positive time for the standard two-phase compressible Euler equations, it is proved that such entropy solution is the sharp interface limit for a family global strong solutions of the modified Jin-Xin relaxation scheme for Navier-Stokes/Allen-Cahn system, here the relaxation time is selected as the thickness of the interface, weighted estimation and improved antiderivative method are used in the proof. Moreover, the simulation results are given by this modified Jin-Xin relaxation scheme method. Both numerical and theoretical results show that, the interacting shock waves can pass through the interface without any effect.
