Multispecies mixing processes play an important role in many engineering, biological, and environmental applications. Since simulating mixing flows can be useful to understand its physics and to study industrial issues, this work aims to develop the basis of a methodology able to simulate the physics of multiple-species mixing flows, using a hybrid large eddy simulation/Lagrangian filtered density function (FDF) method on an adaptive, block-structured mesh. A computational model of notional particles transport on a distributed processing environment is built using a parallel Lagrangian map. This map connects the Lagrangian information with the Eulerian framework of the in-house code MFSim, in which transport equations are solved. The Lagrangian composition FDF method, through the Monte Carlo technique, performs algebraic calculations over an ensemble of notional particles and provides composition fields statistically equivalent to those obtained by finite volume numerical solution of partial differential equations. Finally, to maintain high accuracy in the system of stochastic differential equations solver when an adaptive mesh refinement environment is used, a methodology for ensuring mass conservation is developed to preserve at least the statistical moments up to order two, even in the case of annihilation or cloning of a large number of notional particles in one time step, ensuring the applicability of Lagrangian FDF methods in dynamically adaptive grid refinement.