This paper is concerned with the analytical solutions to the Riemann problem for one-dimensional non-ideal dusty gas flow. We obtain explicitly the elementary wave curves to one-dimensional non-ideal dusty gas flow, and analyze the properties of these wave curves. On the basis of these preparations, by rigorously analyzing the uniqueness and existence of the solution to a system of two nonlinear equations, the analytical solutions are obtained. Besides, the corresponding numerical solutions are also provided. It is shown that the analytical solutions are identical with the corresponding numerical solutions.

中文翻译：

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一维非理想含尘气流的解析解

本文关注的是一维非理想含尘气流的黎曼问题的解析解。我们明确地得到了一维非理想含尘气流的基本波曲线，并分析了这些波曲线的性质。在这些准备工作的基础上，通过严格分析两个非线性方程组解的唯一性和存在性，得到了解析解。此外，还提供了相应的数值解。结果表明，解析解与相应的数值解相同。