This work investigates the rheological behavior of polymer melts under complex 2D flow conditions using a Lagrangian Heterogeneous Multiscale Method (LHMM) [1]. The method combines Dissipative Particle Dynamics (DPD) and Smoothed Particle Hydrodynamics (SPH) to bridge microscopic stress contributions and macroscopic flow dynamics. At the microscale, DPD simulations act as virtual rheometers [2] for polymer melts composed of bead-spring chains (8, 16, and 32 beads per chain). The zero-shear viscosity and shear-thinning behavior obtained from steady-state DPD simulations are fitted to the Carreau–Yasuda model, allowing the definition of a characteristic relaxation time for each melt. Subsequently, a spectral decomposition of the stress relaxation modulus G(t), derived from ensemble-averaged microscopic responses, provides further insight into the viscoelastic behavior across the shear-thinning transition. The spectra exhibit well-defined crossover frequencies and a plateau modulus, consistent with the relaxation times inferred from the Carreau–Yasuda fits and the classical transition from the elastic to the viscous regime. These rheological properties are embedded into the LHMM framework, where local SPH strain rates and velocity gradients are coupled to DPD-based stress responses via the Irving–Kirkwood formalism. The approach is validated in two benchmark problems: Flow Around a Cylinder and Reverse Double Poiseuille flow, for Weissenberg numbers (Wi) in the range 0.5 ≤ Wi ≤ 50 and under low Reynolds number conditions (Re < 1). The methodology captures key non-Newtonian effects, including shear thinning, long-time relaxation, and early signs of flow instabilities. This multiscale strategy enables accurate, predictive modeling of polymeric flows in 2D geometries by integrating microscopic rheological characterization with particle-based solvers. It reveals the fundamental link between microstructure and macroscopic response.