With an increase in the number of Web documents, the number of proposed methods for knowledge discovery on Web documents have been increased as well. The documents do not always provide keywords or categories, so unsupervised approaches are desirable, and topic modeling is such an approach for knowledge discovery without using labels. Further, Web documents usually have time information such as publish years, so knowledge patterns over time can be captured by incorporating the time information. The temporal patterns of knowledge can be used to develop useful services such as a graph of research trends, finding similar authors (potential co-authors) to a particular author, or finding top researchers about a specific research domain. In this paper, we propose a new topic model, Author Topic-Flow (ATF) model, whose objective is to capture temporal patterns of research interests of authors over time, where each topic is associated with a research domain. The state-of-the-art model, namely Temporal Author Topic model, has the same objective as ours, where it computes the temporal patterns of authors by combining the patterns of topics. We believe that such ‘indirect’ temporal patterns will be poor than the ‘direct’ temporal patterns of our proposed model. The ATF model allows each author to have a separated variable which models the temporal patterns, so we denote it as ‘direct’ topic flow. The design of the ATF model is based on the hypothesis that ‘direct’ topic flows will be better than the ‘indirect’ topic flows. We prove the hypothesis is true by a structural comparison between the two models and show the effectiveness of the ATF model by empirical results.