Non-classical non-linear waves exist in dense gases at high pressure in the region close to a thermodynamical critical point. These waves behave precisely opposite to the classical non-linear waves (shocks and expansion fans) and do not violate entropy conditions. More complex EOS other than the ideal or perfect gas equation of state (EOS) is used in describing dense gases. Algorithm development with non-ideal/real gas EOS and application to dense gasses is gaining importance from a numerical perspective. Algorithms designed for perfect gas EOS can not be extended directly to arbitrary real gas EOS with known EOS formulation. Most of the algorithms designed with prefect gas EOS are modified significantly when applied to real gas EOS with the known formulation. These algorithms can become complicated and some times impossible based on the EOS under consideration. The objective of the present work is to develop central solvers with smart diffusion capabilities independent of the eigenstructure and extendable to any arbitrary EOS. Euler equations with van der Waals EOS along with algorithms like MOVERS, MOVERS+, and RICCA are used to simulate dense gasses over simple geometries. Various 1D and 2D benchmark test cases are validated using these algorithms, and the results compared with the data obtained from the literature.

中文翻译：

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使用新颖且稳健的中央求解器对简单几何结构上的稠密气体进行数值模拟

非经典非线性波存在于靠近热力学临界点的区域的高压稠密气体中。这些波的行为与经典的非线性波（激波和膨胀扇）正好相反，并且不违反熵条件。除了理想或完美气体状态方程 (EOS) 之外，更复杂的 EOS 用于描述致密气体。从数值的角度来看，非理想/真实气体 EOS 的算法开发和对致密气体的应用越来越重要。为完美气体 EOS 设计的算法不能直接扩展到具有已知 EOS 公式的任意真实气体 EOS。大多数用完美气体 EOS 设计的算法在应用到具有已知公式的真实气体 EOS 时都得到了显着修改。基于所考虑的 EOS，这些算法可能会变得复杂，有时甚至是不可能的。当前工作的目标是开发具有独立于特征结构的智能扩散能力并可扩展到任何任意 EOS 的中央求解器。使用范德华 EOS 的欧拉方程以及 MOVERS、MOVERS+ 和 RICCA 等算法用于模拟简单几何结构上的致密气体。使用这些算法验证了各种一维和二维基准测试用例，并将结果与​​从文献中获得的数据进行了比较。和 RICCA 用于模拟简单几何结构上的高密度气体。使用这些算法验证了各种一维和二维基准测试用例，并将结果与​​从文献中获得的数据进行了比较。和 RICCA 用于模拟简单几何结构上的高密度气体。使用这些算法验证了各种一维和二维基准测试用例，并将结果与​​从文献中获得的数据进行了比较。