Apparatuses and methods for anaerobic digestion of high-solids waste are provided. The methods may include and the apparatuses may be used for moving the solid waste in a corkscrew-like fashion through a closed container. The method may further include moving the high-solids waste into contact with a heating device to facilitate the corkscrew-like movement. Other methods and apparatuses may use at least one of a partition and a conduit from which liquid or gas is discharged.