A distributed lagrange multiplier based computational method for the simulation of particulate-Stokes flow

In this paper we present a distributed lagrange multiplier (DLM) based Stokes flow algorithm for particulate flows. The entire fluid–particle domain is treated as a fluid. The “fluid” in the particle domain is ensured to move rigidly by adding a rigidity constraint. We modify the SIMPLER (Semi-Implicit Method for Pressure Linked Equations—Revised) algorithm for fluids (by Patankar [Numerical Heat Transfer and Fluid Flow, Taylor and Francis, London, 1980]), to account for the presence of the particle. The modification pertains to the presence of the rigidity constraint in the particle domain. We validate the algorithm with suitable test cases.