A method of stimulating a subterranean formation includes acquiring stimulation treatment input data, simulating a transport of at least one material transport present in a stimulation treatment design with a transport simulator model, determining and preparing the treatment design and performing the stimulating treatment according to the selected treatment design. As recited, simulating includes assuming that for each time stage of the stimulation treatment a velocity field for the at least one material transport and a stimulated flow domain geometry are known and calculating at each time stage the distribution of at least one physical quantity of the at least one material transport using a Lagrangian approach.