A CPU of an analysis apparatus performs a fluid analysis and derives transient distribution information that represents an accumulation distribution of a particulate layer on an inflow-side inner circumferential surface of a honeycomb structure at a time point after a short time interval Δt (step S130). The CPU then repeatedly performs a fluid analysis by taking into account the transient distribution information derived previous time to repeatedly derive transient distribution information (steps S130 to S150) and then derives post-transient-analysis distribution information that represents the accumulation distribution of the particulate layer at a later time point (step S160).