A variable-density fictitious domain method for particulate flows with broad range of particle-fluid density ratios

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 & Patankar [1]. 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. Use of density-weighted reconstruction of the pressure gradients was found to give a stable scheme for high density ratio fluid-particle systems. Various verification and validation test cases on fixed and freely moving particles are performed to show that the numerical approach is accurate and stable for a wide range (10−3 − 10) of particle-fluid density ratios.