Since volcanic eruptions are events that can greatly endanger human lives and disrupt human activities such as air traffic, it is of major interest to simulate such phenomena. Volcanic ash transport and dispersion models typically describe particle motion in a turbulent velocity field. Volcanic particles (known as tephra) are advected inside this field from the moment they leave the vent of the volcano until they deposit on the ground. We developed a flexible simulation tool called TETRAS (TEphra TRAnsport Simulator) based on a hybrid Eulerian-Lagrangian model. As this kind of model needs computationally intensive simulations, a parallelization on a distributed memory architecture was developed. Volcanic eruptions involve phenomena occurring at multiple temporal and spatial scales, such as fast rising of particles inside the volcanic column, transport of fine particles over very long range or aggregation of fine particles into larger ones. Thus, we developed a multiscale implementation of the software using MMSF (Multiscale Modeling and Simulation Framework) techniques and tools. This implementation combines short and long-range transport of particles as well as particle aggregation. In this paper, we show the multiscale aspect of the design and implementation. Then, we tackle two load balancing problems that arise from this model: first at the transport code level, where unequal distribution of particles inside the domain directly leads to different load for processors if a naive work distribution is chosen; second at the multiscale level, where the resource allocation for each submodel must be chosen wisely to achieve optimal performances.