A Variable-Density Fictitious-Domain Method for Fully Resolved Simulation of High-Density Ratio Fluid-Particle Systems

A numerical scheme for fully resolved simulation of fluid-particle systems with freely moving rigid particles is developed. The approach is based on a fictitious domain method wherein the entire fluid-particle domain is assumed to be an incompressible fluid but with variable density. The flow inside the particle domain is constrained to be a rigid body motion using an additional rigidity constraint in a fractional step scheme. The rigidity constraint force is obtained based on the fast computation technique proposed by Sharma and Patankar (2005). The particle is assumed to be made up of material points moving on a fixed background mesh where the fluid flow equations are solved. The basic finite-volume solver is based on a co-located grid incompressible but variable density flow. The incompressibility constraint is imposed by solving a variable-coefficient pressure equation giving rise to a stable scheme for high density ratio fluid-particle systems. Through various verification and validation test cases on fixed and freely moving particles it is shown that the numerical approach is accurate and stable for a wide range of fluid-particle density ratios.