标题： 零阶一致性残差和保守SPH流体动力学的背景压力 显示英文标题

标题： On zero-order consistency residue and background pressure for the conservative SPH fluid dynamics

摘要： 作为保守平滑粒子流体动力学（SPH）方法的主要挑战之一，零阶一致性问题虽然被认为可以通过粒子正则化方案如输运速度公式得到缓解，但在层流和湍流模拟中，显著地抑制了长通道中的流动。 在此发现的基础上，本文不仅全面分析了这种压力驱动通道流中的抑制原因，还将该问题与重力驱动自由表面流中的过度数值耗散联系起来。 在两种典型的流动场景中，非物理数值抑制的共同根本原因是零阶梯度一致性残差，这一原因被揭示出来。 对于两种场景中背景压力对残差的不利影响进行了揭示和讨论。 为了全面理解残差的行为并减轻其潜在的不利影响，我们进行了理论分析和数值实验，重点研究了关键敏感因素。 为了研究重力驱动自由表面流中由残差引起的非物理能量耗散，在无粘性驻波情况下测试了水深和输入动态压力。 为了调查压力驱动通道流中的速度损失，我们检查了通道长度、分辨率和出口压力的影响。 介绍了适用于两种典型流动的最先进的反向核梯度校正技术，并证明该技术在减少残差效应方面是有效的，但我们发现其校正能力从根本上受到限制。 最后，对FDA喷嘴这一工程基准进行了测试，以展示复杂几何中的残差影响，突显了在不可避免高背景压力场景中校正方案的必要性。 显示英文摘要

摘要： As one of the major challenges for the conservative smoothed particle hydrodynamics (SPH) method, the zero-order consistency issue, although thought to be mitigated by the particle regularization scheme, such as the transport velocity formulation, significantly damps the flow in a long channel for both laminar and turbulent simulations. Building on this finding, this paper not only thoroughly analyzes the damping reason in this pressure-driven channel flow, but also relates this problem with the excessive numerical dissipation in the gravity-driven free-surface flow. The common root cause of the non-physical numerical damping in the two typical flow scenarios, the zero-order gradient consistency residue, is exposed. The adverse influence of the background pressure on the residue for the two scenarios is revealed and discussed. To comprehensively understand the behavior of the residue and mitigate its potential adverse effects, we conduct both theoretical analysis and numerical experiments focusing on the key sensitive factors. For studying the residue-induced non-physical energy dissipation in the gravity-driven free-surface flow, the water depth and input dynamic pressure in the inviscid standing wave case are tested. To investigate the velocity loss in the pressure-driven channel flow, we examine the effects of the channel length, resolution, and outlet pressure. The state-of-the-art reverse kernel gradient correction technique is introduced for the two typical flows, and proved to be effective in reducing the residue effect, but we find its correction capability is fundamentally limited. Finally, the FDA nozzle, an engineering benchmark, is tested to demonstrate the residue influence in a complex geometry, highlighting the necessity of correction schemes in scenarios with unavoidable high background pressure.