New semi-Lagrangian-based PISO method for fast and accurate indoor environment modeling

Fast airflow and heat transfer simulation is becoming increasingly more and more important in building design, real-time system control, and emergent environment management. Conventional algorithms such as SIMPLE or PISO need great calculation effort and thus cannot meet the requirement of computing speed. Some developed fast calculation methods such as FFD lack prediction accuracy due to the inherent simplifications. This paper developed a new fast computational method named semi-Lagrangian PISO (SLPISO) that integrates the semi-Lagrangian scheme with a PISO solver. The SLPISO solver can significantly reduce the computational cost compared to SIMPLE and PISO while maintaining the required accuracy. The accuracy and stability of the developed algorithm were analysed. A confined space lid-driven cavity flow case and a mixing convection case in a confined space were used to evaluate and illustrate method performance. Results reveal that SLPISO possesses similar accuracy to PISO but can tolerate much larger time steps in the transient simulation. A larger time step will increase the false diffusion, and thus smooth the gradients of the flow field. A proper diffusion coefficient corresponding with a given time step is, hence, necessary to obtain accurate results.