Multi-phase flows are part of our natural environment such as tornadoes, typhoons, air and water pollution or volcano activities as well as of industrial technology such as power plants, combustion engines, propulsion systems, or chemical and biological industry. The industrial use of multi-phase systems requires analytical and numerical strategies for predicting their behavior. In its second extended edition this book contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations. This book provides a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics. In the present second volume the mechanical and thermal interactions in multiphase dynamics are provided. This second edition includes various extensions, improvements and corrections.