In this work we propose two parallel implementations of numerical method for the two-dimensional advection-coagulation equation: pure CPU and hybrid CPU/GPU. We approximate the advection component across the two dimensional space with use of unstructured grid and finite volume method with flux limiters. Smoluchowski coalescence operator corresponds to the coagulation process. We evaluate it within low complexity ($$O (N \log N)$$) via exploitation of the low-rank skeleton decomposition of coagulation kernel. We decompose spatial grid into the subdomains and solve the model equation in parallel using MPI. Even though we exploit the fast methods for evaluation of coalescence operator it is the most time-consuming part of numerical algorithm. Hence, we test performance of GPU accelerators for corresponding Smolushowski integrals. All in all, we evaluate the efficiency of incorporating MPI and Nvidia CuFFT library for speedup of calculations and obtain almost linear scalability of MPI implementation of our algorithm. We also find that hybrid exploitation of CPUs and GPUs leads to additional speedup of computations by 2–4 times.