This paper presents a formulation of a general form of an equation for pressure using thermodynamic principles. The motivation for this is in large part due to the need for a pressure equation for smoothed particle hydrodynamics, SPH, that takes into account the role of entropy. This is necessary because the use of physical and artificial viscosity leads to an increase in entropy. While such an increase in entropy in liquids may be negligibly small, standard SPH formulations treat a liquid as a weakly compressible gas. Consequently, for fluid–fluid and fluid–structure impact flows, the resulting increase in entropy is not negligible anymore. The proposed pressure equation contains diffusion terms whose main role is to smooth out unphysically large numerical oscillations in the pressure field related to the shock during an impact event. One consequence of adopting this numerical scheme, however, is that there are new (free) parameters that must be set. Nevertheless, effort has been made to obtain their plausible estimators from physical principles. The proposed model is also applicable outside the domain of SPH.

本文提出了使用热力学原理的压力方程的一般形式的公式。这样做的动机在很大程度上是由于需要考虑熵的作用的平滑粒子流体动力学 SPH 的压力方程。这是必要的，因为使用物理和人工粘度会导致熵增加。虽然液体中熵的这种增加可能小到可以忽略不计，但标准 SPH 公式将液体视为弱可压缩气体。因此，对于流体 - 流体和流体 - 结构碰撞流，由此产生的熵增加不再可以忽略不计。所提出的压力方程包含扩散项，其主要作用是消除与撞击事件期间的冲击相关的压力场中非物理大的数值振荡。然而，采用这种数值方案的一个后果是必须设置新的（自由）参数。尽管如此，人们已经努力从物理原理中获得它们的合理估计量。所提出的模型也适用于 SPH 领域之外。