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.
Bibliographical noteFunding Information:
This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korea government ( MSIP ) ( NRF-2014R1A2A2A01006544 , NRF-2014R1A2A1A11053140 , and NRF-20151009350 ) and in part by the Yonsei University Future–leading Research Initiative of 2014.
© 2016 Elsevier Inc.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Modelling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics