论文标题
riemann的问题与单点加热源的恒定流量
Riemann problem for constant flow with single-point heating source
论文作者
论文摘要
这项工作着重于具有全球恒定初始条件和单点加热源的Euler方程问题，这来自加热一维无关可压缩恒定流量的物理问题。为了处理Dirac Delta功能的来源，我们提出了一个双重经典Riemann问题（CRPS）耦合的分析框架，该框架将加热点两侧的流体视为两个单独的Riemann问题，然后将其耦合。在双重CRP框架下，该解决方案是自相似的，只有三种类型的解决方案。理论分析也得到了数值模拟的支持。此外，建立了Riemann解决方案的唯一性，对初始条件的马赫数有一些限制。
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.
