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 particle–fluid systems with freely moving rigid particles is developed. The approach is based on a fictitious domain method wherein the entire particle–fluid 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) [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 particle–fluid 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 6 ) of particle–fluid density ratios.