A decoupled monolithic projection method for natural convection problems

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• 作者：Xiaomin Pan^a ; ^{sanhepanxiaomin@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Kyoungyoun Kim^b ; ^{kkim@hanbat.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Changhoon Lee^a ; ^c ; ^{clee@yonsei.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Jung-Il Choi^a ; ^{jic@yonsei.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Projection method ; Monolithic approach ; Approximate block LU decomposition ; Natural convection ; Temporal second-order accuracy
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：1 June 2016
• 年：2016
• 卷：314
• 期：Complete
• 页码：160-166
• 全文大小：521 K

文摘

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.