Re-definition of Navier boundary condition: development of the hydrodynamic boundary condition on the solid surface

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K03929
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 19010:Fluid engineering-related
• Research Institution: Osaka Metropolitan University (2022); Osaka City University (2020-2021); Osaka University (2018-2019)
• Principal Investigator: Omori Takeshi 大阪公立大学, 大学院工学研究科, 准教授 (70467546)
• Co-Investigator(Kenkyū-buntansha): 山口 康隆 大阪大学, 大学院工学研究科, 准教授 (30346192)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: 固液摩擦 / 滑り長さ / 非平衡統計力学 / Green-Kubo積分 / Navier境界条件 / 動的濡れ / 分子動力学

Outline of Final Research Achievements

The hydrodynamic boundary condition (BC) consists of two elements: not only the constitutive equation for the condition but the boundary position where the condition should be imposed (the hydrodynamic wall position, HWP) need to be specified. As the constitutive equation, we employed Navier BC (NBC) assuming the wall shear stress is proportional to the slip velocity, and developed methods to determine both the HWP and the solid-liquid friction coefficient (FC), the proportionality coefficient in NBC, on our theoretical basis. We applied the present methods to a number of molecular dynamics (MD) simulation data and showed their significant advantages over the conventional methods, which usually fail to calculate correct FCs from MD simulation data. We have also developed a numerical scheme to apply NBC on arbitrary shaped walls in computational fluid dynamics, which can be used for flow prediction e.g. in fine and complex coduits.

Free Research Field

流体工学

Academic Significance and Societal Importance of the Research Achievements

本研究は，流体運動に対する壁面境界条件を課すべき位置は壁面とは異なりNavier-Stokes方程式が成立する領域外縁であるということを初めて明確に示し，境界位置と境界条件に含まれる未定係数の計測方法についても提案したものである．また，分子動力学解析によって求めた壁面摩擦応力の自己相間関数をGreen-Kubo積分すると収束値がゼロになってしまう（実はこれも正しくなく実際にはゼロにはならない）という「プラトー（Plateau）問題」を解決した点は流体力学だけでなく非平衡統計力学における意義も大きいと考える．