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• W4225429166 abstract "• We developed a monolithic projection-based method for natural convection problems. • Non-Oberbeck–Boussinesq (NOB) approximation is considered in the problems. • The proposed method uses the Crank–Nicolson scheme with staggered time stepping. • A pressure-correction scheme is used for the variable-coefficient Poisson equation. • We investigated the effects of NOB approximation on 2D and 3D problems. This paper presents an efficient monolithic projection-based method with staggered time discretization (MPM-STD) to examine the non-Oberbeck–Boussinesq (NOB) effects in several natural convection problems involving dramatic temperature-dependent changes in fluid properties. The proposed approach employs the Crank–Nicolson scheme along with staggered time discretization to discretize the momentum and energy equations. The momentum and energy equations are decoupled by evaluating the velocity vector at integral time levels ( n + 1 ), and the scalar variables (pressure and temperature) at half-integral time levels ( n + 1 2 ). The observed density variations in all terms result in a variable-coefficient Poisson equation, which is difficult to solve efficiently. The convergence is accelerated via adoption of an appropriate pressure-correction scheme that transforms the aforementioned Poisson equation to a constant-coefficient form. The numerical simulations concerning two-dimensional (2D) periodic NOB Rayleigh–Bénard convection (RBC) in glycerol and 2D differentially heated cavity (DHC) problem in air confirmed the second-order temporal and spatial accuracies of the proposed method. By simulating the 2D DHC problem in air and the RBC problem in liquid (water or glycerol) considering NOB effects, it is concluded that the proposed MPM-STD significantly mitigates the time-step restriction, thereby increasing the computational efficiency, which exceeds that of existing semi-implicit and explicit schemes. Moreover, the potential of the proposed approach with regard to solving challenging three-dimensional (3D) turbulent problems is demonstrated by performing direct simulations of turbulent RBCs under NOB effects involving temperature differences up to 60 K with a corresponding Rayleigh number ( Ra = 10 6 )." @default.
• W4225429166 created "2022-05-05" @default.
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• W4225429166 date "2022-08-01" @default.
• W4225429166 modified "2023-09-30" @default.
• W4225429166 title "Monolithic projection-based method with staggered time discretization for solving non-Oberbeck–Boussinesq natural convection flows" @default.
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• W4225429166 doi "https://doi.org/10.1016/j.jcp.2022.111238" @default.
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