The paper presents the theoretical basis for the extension of the V π LES method, originally developed in recent works of the authors for incompressible flows, to flows with variable density and transport properties but without chemical reactions. The method is based on the combination of grid based and grid free computational particle techniques. Large scale motions are modelled on the grid whereas the fine scale ones are modelled by particles. The particles represent the fine scale vorticity, and scalar quantities like e.g., temperature, mass fractions of species, density and mixture fraction. Coupled system of equations is derived for large and fine scales transport.