Implementation of three-dimensional physical reflective boundary conditions in mesh-free particle methods for continuum fluid dynamics: Validation tests and case studies

Abstract

Mesh-free particle methods applied to continuum fluid dynamics still use fictitious, ghost or virtual particles, and/or molecular dynamics concepts in the treatment of the boundaries. The aim of this paper is to present the implementation of the physical reflective boundary conditions (RBC), based on Newton’s restitution law and the foundations of analytical geometry, in the treatment of contours in a three-dimensional (3D) domain. In a previous paper [C. A. D. Fraga Filho, “An algorithmic implementation of physical reflective boundary conditions in particle methods: Collision detection and response,” Phys. Fluids 29, 113602 (2017)], RBC validation tests and simulation results were presented for a two-dimensional (2D) domain. The current work presents the validation of the collision detection and response algorithm employed for the RBC and its application in two cases (hydrostatics and hydrodynamics) in a 3D domain. Following an analysis of the simulation results, the applicability of the RBC to 3D continuum fluid dynamic problems is verified. In the hydrostatics case, a still liquid (Newtonian, incompressible, uniform, and isothermal) inside an immobile reservoir is studied. The fluid flow is modeled using an improved Smoothed Particle Hydrodynamics (SPH) formulation utilizing a modified concept of pressure. The simulation results are excellent, showing complete agreement with the analytical solution and the nonmotion of the particles throughout the simulation time. In the hydrodynamics case, 3D dam break flow modeling is carried out using the standard SPH formulation. Results provided by the RBC and standard SPH modeling are compared with the literature data demonstrating good agreement with the experimental findings.