Seminar| Institute of Mathematical Sciences
Time: Thursday, December 19th, 2024,15:30-16:30
Location: IMS, RS408
Speaker:Xiaomin Pan, Shanghai University
Abstract:An advanced monolithic projection-based method equipped with staggered time discretization (MPM-STD) has been crafted to probe into the non-Oberbeck–Boussinesq (NOB) effects within a diverse array of natural convection conditions, notably where fluid properties significantly alter with temperature. Employing the Crank–Nicolson scheme in tandem with staggered time discretization for momentum and energy equations enables the decoupling of these equations. This approach directly addresses the complexity of the variable coefficient Poisson equation through an innovative pressure-correction scheme, converting it into a constant coefficient equation for enhanced computation efficiency. Through numerical tests in two-dimensional periodic NOB Rayleigh–Bénard convection (RBC) with glycerol, the MPM-STD's second-order accuracy and efficiency were validated. The application of this method to differentially heated cavity problems in air and RBC in liquids under NOB effects demonstrated its capacity to significantly mitigate timestep constraints and enhance computational efficiency, surpassing conventional semi-implicit and explicit techniques. Additionally, the application of MPM-STD to challenging three-dimensional turbulence scenarios, as evidenced in direct simulations of turbulent RBC under NOB effects, exemplifies its robustness and potential for tackling complex fluid dynamics investigations. The method's extensive applicability, including the study of NOB effects in RBC with various aspect ratios and under different conditions, underscores its adaptability and comprehensive utility in addressing intricate fluid dynamics challenges.