CAJ | 학술논문

由于Lagrange粒子法的本质，固壁边界条件的施加一直是光滑粒子动力学方法的难点之一。本文从固壁边界的物理原理出发，应用多层虚粒子表征固壁边界，提出了一种新型固壁边界施加模型。将虚粒子看作流体的扩展，计算中虚粒子密度保持不变，压力、速度等参数通过对流体粒子的插值获得，虚粒子有条件的参与控制方程的计算，对流体的密度/压力产生影响，通过压力梯度隐式地表征壁面与流体之间的作用强度并对流体粒子施加沿壁面法线方向的斥力作用，防止流体粒子对壁面的穿透。数值算例测试结果表明，与现有固壁边界施加方法相比，本文方法更加符合流体与固壁边界作用的物理原理，可以简单、有效地施加固壁边界条件，方便地应用于具有复杂几何边界的问题，获得稳定的流场形态、规则的粒子秩序及良好的速度、压力等参量的分布。
유우Lagrange입자법적본질，고벽변계조건적시가일직시광활입자동역학방법적난점지일。본문종고벽변계적물리원리출발，응용다층허입자표정고벽변계，제출료일충신형고벽변계시가모형。장허입자간작류체적확전，계산중허입자밀도보지불변，압력、속도등삼수통과대류체입자적삽치획득，허입자유조건적삼여공제방정적계산，대류체적밀도/압력산생영향，통과압력제도은식지표정벽면여류체지간적작용강도병대류체입자시가연벽면법선방향적척력작용，방지류체입자대벽면적천투。수치산례측시결과표명，여현유고벽변계시가방법상비，본문방법경가부합류체여고벽변계작용적물리원리，가이간단、유효지시가고벽변계조건，방편지응용우구유복잡궤하변계적문제，획득은정적류장형태、규칙적입자질서급량호적속도、압력등삼량적분포。
As the smoothed particle hydrodynamics (SPH) is a truly Lagrangian meshfree method, the implementation of solid boundary condition has been one of the key problems that hinder SPH from applying to lots of engineering problems. In order to treat the boundary conditions e?ciently, based on the boundary-fluid interaction principles, a new boundary treatment method is proposed. In this method, the solid boundary is represented implicitly by several layers of dummy particles along the boundary line. During the simulation, the dummy particles are treated as an extension of the fluid phase. The densities of dummy particles are kept constant, and the pressures and velocities are interpolated from the nearby fluid particles at each time step. Dummy particles can be involved in the calculation of the continuity equation conditionally and exert influences on the density/pressure field of the fluid phase. Then, for the fluid particles that approach the solid boundary, local pressure gradients are used to represent the dummy-fluid particle pair’s interaction strength and act as the boundary force term implicitly, which is tuned to be repulsive only and normal to the boundary. Thus, large pressure gradients mean strong boundary-fluid interaction strength, and the boundary force from the dummy particles should also be large enough to prevent the fluid particles from penetrating the solid boundary;and on the contrary, small pressure gradients mean weak boundary-fluid interaction strength and the boundary force becomes soft and little disturbs the flow field. Results of numerical tests demonstrate that, compared with the existing boundary treatment methods, the new method is in better accordance with the physical principles of the fluid-boundary interaction, and is able to treat arbitrary solid boundaries with limited modeling and computational costs. With the help of this new boundary treatment method, the stable flow field, well-ordered particle distribution, smooth velocity and pressure fields could be obtained. Theoretically, this new boundary treatment method could be directly used in three-dimensional multi-phase problems. Further tests are planned to be carried out; meanwhile, expanding the new boundary treatment method to rigid-fluid interaction problems is also a work in the future.