In this seminar I am going to discuss things I've learnt as a PhD student working on moment methods in kinetic gas theory. I am going to

• talk briefly about the history of Moment method and its scope in modelling gas flows,
• then discuss moment method using abstract notation,
• then introduce a concrete moment system (3D R13 moment system) and discuss a case study (Crooks radiometer simulation),
• then discuss first-order formulation of moment systems,
• then discuss generic moment systems and its derivation using precise definitions,
• then discuss a generic FEM-based numerical framework to solve these generic moment systems,
• then discuss several simulation cases (flow over a sphere, lid driven cavity, non-isothermal cavity flow) solved using this generic formulation,
• and finally conclude by discussing what could be done next.