Trans-Kyushu Limited Express (Kyushu Odan Tokkyu=九州横断特急) connects both west and east coast of Kyushu. It connects Beppu, Oita and Kumamoto. The biggest volcano, Mt. Aso is located in the middle of this trains’ route.
Due to a huge damage by earthquake, a part of Houhi line between Aso and Kumamoto is closed. This train runs only between Beppu, Oita and Aso until further notice.
These trains connect Hakata (博多) with Yufuin (由布院) and Oita (大分) or Beppu (別府). Yufuin is one of the most popular hot springs resort in Kyushu. This is the train that you need to take when you go to Yufuin. Of course these train’s name are named from Yufuin. “Yufuin no Mori” means Yufuin’s forest. These two trains are operated on same route and fully covered by JR Pass. But Yufuin no Mori is operated by the specialized car, KIHA-71 or 72 series. This express train is one of the best in JR Kyushu train and very very popular. So I strongly recommend to take Yufuin no Mori, not Yufu.
This limited express train is one of most popular limited express train that is serviced by JR Kyushu. This connects Hakata and Kokura with Oita and Saeki. If you go to the popular hot springs resort, Beppu, this train is that you need to take after you get off Shinkansen at Kokura or Hakata. Of course this train is fully covered by Japan Rail Pass.