In this report, transport problems are solved with a particle method that takes into account the Eulerian background flow field. Dispersion and other transport problems can be solved applying this model, as long as the corresponding transport process is formulated with a flux gradient relation, i.e., the advection-diffusion equation. The particle method has been made consistent with such a transport process. Since many 3D flow models are formulated in general coordinates, the 3D particle displacements are also given with respect to such a coordinate system. Analytical and numerical aspects of this particle method have been studied. The effectiveness of the method has been demonstrated with two academic test cases including streamlines in a recirculation zone and grid dependency in a discharge problem.