Violeau D
Saint-Venant Laboratory for Hydraulics, Université Paris-Est, Joint Research Unit EDF R&D, CETMEF, Ecole des Ponts, 6 quai Watier, 78400 Chatou, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 2):036705. doi: 10.1103/PhysRevE.80.036705. Epub 2009 Sep 25.
An investigation of dissipative forces for Lagrangian computational fluid dynamics is conducted from Hamiltonian considerations including energy dissipation for macroscopic systems. It is shown that discrete forces must fulfill particular rules to be in agreement with the fundamentals of Physics. Those rules are specified in the case of the smoothed particle hydrodynamics (SPH) numerical approach, leading to a clear treatment of friction forces in connection with energy dissipation. In particular, it is proved that the kernel function, which is at the heart of interpolation in SPH, must satisfy some constraints in order to be consistent with the dissipative properties of a real fluid. A numerical example is given to illustrate the abovementioned considerations.
从哈密顿原理出发，包括宏观系统的能量耗散，对拉格朗日计算流体动力学中的耗散力进行了研究。结果表明，离散力必须满足特定规则，才能与物理学基本原理相一致。在光滑粒子流体动力学（SPH）数值方法的情况下，这些规则被明确规定，从而能够清晰地处理与能量耗散相关的摩擦力。特别是，证明了作为SPH插值核心的核函数必须满足一些约束条件，以便与真实流体的耗散特性相一致。给出了一个数值例子来说明上述考虑因素。
