In this work, to rectify the equation of state (EOS) of a recently introduced constant speed entropic kinetic model (CSKM), a virtual force method is proposed. The CSKM, as shown in Zadehgol and Ashrafizaadeh [J. Comp. Phys. 274, 803 (2014)] and Zadehgol [Phys. Rev. E 91, 063311 (2015)], is an entropic kinetic model with unconventional entropies of Burg and Tsallis. The dependence of the pressure on the velocity, in the CSKM, was addressed and it was shown that it can be rectified by inserting rest particles into the model. This work shows that this dependence can also be removed by treating the pressure gradient as a pseudo force term, expanding the source term using the Fourier series, and applying the modified method of Khazaeli et al. [Phys. Rev. E 98, 053303 (2018)]. The proposed method can potentially be used to remove other pseudo-force error terms of the CSKM, e.g. the residual error terms which become significant at high Mach numbers, ensuring thermodynamic consistency of the entropic model, at the compressible flow regimes. The accuracy of the method is verified by simulating benchmark flows.

中文翻译：

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一种修正格子Boltzmann模型状态方程的虚力法

在这项工作中，为了纠正最近引入的恒速熵动力学模型（CSKM）的状态方程（EOS），提出了一种虚拟力方法。CSKM，如 Zadehgol 和 Ashrafizaadeh [J.比较。物理。 274, 803 (2014)] 和 Zadehgol [物理。牧师 E 91, 063311 (2015)]，是一个熵动力学模型，具有 Burg 和 Tsallis 的非常规熵。在 CSKM 中，压力对速度的依赖性得到了解决，并且表明可以通过将静止粒子插入模型来纠正它。这项工作表明，这种依赖性也可以通过将压力梯度视为伪力项、使用傅里叶级数扩展源项以及应用 Khazaeli 的改进方法来消除等。[物理。牧师 E 98, 053303 (2018)]。所提出的方法可以潜在地用于去除 CSKM 的其他伪力误差项，例如在高马赫数下变得显着的残余误差项，确保熵模型在可压缩流动状态下的热力学一致性。通过模拟基准流验证了该方法的准确性。