A method of detecting and mitigating flow instabilities, such as slugging, in hydrocarbon production wells. Real-time production data pertaining to each well is are retrieved. Using the production data, patterns of flow instability are identified therein. A numerical model of transient and thermal multiphase flow in each well is generated. Well test data is are retrieved from a database. The numerical model is calibrated using the well test data. Using the calibrated numerical model, a parametric study is performed to determine how input parameters affect at least one of stability and performance of the wells. Results of the parametric study are queried to determine a type of flow instability and to determine operating conditions to improve performance of the wells. An advisory is provided to a user to change operating conditions of one or more of the wells, to improve stability and/or performance of one or more of the wells.