单点热源定常流的黎曼问题
Riemann problem for constant flow with single-point heating source
摘要：
本文研究了具有全局常初值和单点热源的Euler方程组的黎曼问题，该问题来源于加热一维无粘可压缩常流的物理问题。为了解决狄拉克δ函数的来源问题，提出了一种双经典黎曼问题（CRPs）耦合的分析框架，将加热点两侧的流体看作两个独立的黎曼问题，然后将它们耦合起来。在双CRPs框架下，解是自相似的，并且只存在三种类型的解，理论分析也得到了数值模拟的支持。此外，在对初始条件马赫数作一定限制的条件下，证明了Riemann解的唯一性。
英文摘要：
This work focuses on the Riemann problem of Euler equations with global constant initial conditions and a single-point heating source, which comes from the physical problem of heating one-dimensional inviscid compressible constant flow. In order to deal with the source of Dirac delta-function, we propose an analytical frame of double classic Riemann problems(CRPs) coupling, which treats the fluids on both sides of the heating point as two separate Riemann problems and then couples them. Under the double CRPs frame, the solution is self-similar, and only three types of solution are found. The theoretical analysis is also supported by the numerical simulation. Furthermore, the uniqueness of the Riemann solution is established with some restrictions on the Mach number of the initial condition.
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