This paper proposes the User Viewing Flow Modeling (SINGLE) method for the article recommendation task, which models the user constant preference and instant interest from user-clicked articles. Specifically, we employ a user constant viewing flow modeling method to summarize the user's general interest to recommend articles. We utilize Large Language Models (LLMs) to capture constant user preferences from previously clicked articles, such as skills and positions. Then we design the user instant viewing flow modeling method to build interactions between user-clicked article history and candidate articles. It attentively reads the representations of user-clicked articles and aims to learn the user's different interest views to match the candidate article. Our experimental results on the Alibaba Technology Association (ATA) website show the advantage of SINGLE, which achieves 2.4% improvements over previous baseline models in the online A/B test. Our further analyses illustrate that SINGLE has the ability to build a more tailored recommendation system by mimicking different article viewing behaviors of users and recommending more appropriate and diverse articles to match user interests.