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A decoupled monolithic projection method for natural convection problems. (English) Zbl 1349.76518
Summary: We propose an efficient monolithic numerical procedure based on a projection method for solving natural convection problems. In the present monolithic method, the buoyancy, linear diffusion, and nonlinear convection terms are implicitly advanced by applying the Crank-Nicolson scheme in time. To avoid an otherwise inevitable iterative procedure in solving the monolithic discretized system, we use a linearization of the nonlinear convection terms and approximate block lower-upper (LU) decompositions along with approximate factorization. Numerical simulations demonstrate that the proposed method is more stable and computationally efficient than other semi-implicit methods, preserving temporal second-order accuracy.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76R10 Free convection
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