Two Second-Order Ecient Numerical Schemes for the Boussinesq EquationsOA北大核心
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
LIU Fang;WANG Danxia;ZHANG Jianwen
School of Mathematics,Taiyuan University of Technology,Jinzhong 030600,ChinaSchool of Mathematics,Taiyuan University of Technology,Jinzhong 030600,China Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology,Jinzhong 030600,ChinaSchool of Mathematics,Taiyuan University of Technology,Jinzhong 030600,China Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology,Jinzhong 030600,China
数学
Scalar auxiliary variable approachPressure-correction methodFully decoupledUnconditional stabilityBoussinesq equations
《应用数学》 2025 (1)
P.114-129,16
Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
评论