Small dust grain dynamics on adaptive mesh refinement grids

Context. Small dust grains are essential ingredients of star, disk and planet formation. Aims. We present an Eulerian numerical approach to study small dust grain dynamics in the context of star and protoplanetary disk formation. It is designed for finite volume codes. We use it to investigate dust dynamics during the protostellar collapse. Methods. We present a method to solve the monofluid equations of gas and dust mixtures with several dust species in the diffusion approximation implemented in the adaptive-mesh-refinement code RAMSE