A simple analytical model of complex wall in multibody dissipative particle dynamics

In the context of multibody dissipative particle dynamics (MDPD), a closed-form mathematical expression is developed to analytically model a complex wall. MDPD is a modified version of dissipative particle dynamics (DPD), a particle-based mesh free method. There have been several attempts to analytically model the influence of solid walls and non-periodic boundary conditions in the DPD approach. However, there is a limited number of studies for these boundary conditions associated with MDPD that capture static and dynamic fluid-structure interactions through direct modeling of fluid-solid particle interactions. This work, for the first time, employs an analytical model (integral approach) for the solid wall boundary condition in MDPD that brings substantial gain in computational efficiency and thus expands the scope of its applicability to curved or complex walls. Furthermore, a modified model of conservative force is used in the current investigation. The model is first normalized to address the discrepancies in wetting that exist in the present literature and is then validated through several benchmark studies and test cases, such as a Wenzel model. Moreover, comparisons between both the fully numerical and the semi-analytical (integral force model) approaches are drawn. Time efficiency, accuracy, density fluctuation in vicinity of solid wall, and limitations of the proposed model are thoroughly discussed.