Particle-laden turbulent flows have diverse engineering applications, primarily stemming from spray settings. However, experimental techniques and numerical methods face significant challenges in capturing all the scales of fluid-particle interaction. To address this issues, we aim to develop a methodology for simulating and analyzing the particle-laden turbulent jet flow in the two-way coupling regime of mass, momentum, and energy. A crucial aspect of point particle methods is modelling particles' interactions with the carrier phase. This is often achieved by additional terms to the system of equations as the product of Dirac deltas centered on the dispersed phase and interface fluxes, where the localization via a Dirac delta and the expressions of the coupling fluxes are usually justified by intuition. However, these expressions can be derived from the underlying equations. With the hypotheses of: scale separation of carrier flow into a macroscopic component and a microscopic linear disturbance, and considering the microscale linear problem and the method of Green's functions, an analytic expression of the expected form is obtained. Then, the singular Dirac deltas are regularized by finding the Green's functions that describe their propagation, so their effect can be represented at a later time when the singularity has spread out. The particles' equations are obtained by integrating the underlying evolution equations on their dynamic control volume. They couple with the carrier phase by the fluxes they exchange at the interface, for which closure models need to be provided. Numerical simulations of an incompressible jet with rigid particles were made using an in-house code. The results show alterations of the overall jet behavior and preservation of universal properties such as self-similarity of axial velocity profiles. These findings suggest that many important jet properties can be described using low-order models, even for dispersed multiphase flows.