Fully decoupled monolithic projection method for natural convection problems

6 To solve time-dependent natural convection problems, we propose a fully decoupled monolithic projection method. 7 The proposed method applies the Crank–Nicolson scheme in time and the second-order central finite difference 8 in space. To obtain a non-iterative monolithic method from the fully discretized nonlinear system, we first adopt 9 linearizations of the nonlinear convection terms and the general buoyancy term with incurring second-order errors 10 in time. Approximate block lower-upper decompositions, along with an approximate factorization technique, are 11 additionally employed to a global linearly coupled system, which leads to several decoupled subsystems, i.e., a fully 12 decoupled monolithic procedure. We establish global error estimates to verify the second-order temporal accuracy of 13 the proposed method for velocity, pressure, and temperature in terms of a discrete l-norm. Moreover, according to 14 the energy evolution, the proposed method is proved to be stable if the time step is less than or equal to a constant. 15 In addition, we provide numerical simulations of two-dimensional Rayleigh–Bénard convection and periodic forced 16 flow. The results demonstrate that the proposed method significantly mitigates the time step limitation, reduces the 17 computational cost because only one Poisson equation is required to be solved, and preserves the second-order temporal 18 accuracy for velocity, pressure, and temperature. Finally, the proposed method reasonably predicts a three-dimensional 19 Rayleigh–Bénard convection for different Rayleigh numbers. 20