The time viscosity-splitting method for the Boussinesq problem
In this article, we consider the time viscosity-splitting method for the Boussinesq problem. By using this technique, the considered problem is decoupled into two subproblems, and each subproblem is solved more easily than the original one. In the first step, two linear elliptic problems with semi-i...
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| Veröffentlicht in: | Journal of mathematical analysis and applications Jg. 445; H. 1; S. 186 - 211 |
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| Abstract | In this article, we consider the time viscosity-splitting method for the Boussinesq problem. By using this technique, the considered problem is decoupled into two subproblems, and each subproblem is solved more easily than the original one. In the first step, two linear elliptic problems with semi-implicit schemes for the convection terms are solved. The advantage of using such numerical technique is that a linear system with the constant coefficient matrices is obtained and then the computation becomes easy. In the second step, a system consists of a Stokes problem and a linear elliptic problem is solved. The main results of this article include that (1) Establish the stability of numerical solutions in the time viscosity-splitting method; (2) Provide the convergence results of strongly second order for the velocity and temperature and strongly first order for the pressure. Finally, some numerical results are provided to display the performances of the developed numerical algorithms. |
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| AbstractList | In this article, we consider the time viscosity-splitting method for the Boussinesq problem. By using this technique, the considered problem is decoupled into two subproblems, and each subproblem is solved more easily than the original one. In the first step, two linear elliptic problems with semi-implicit schemes for the convection terms are solved. The advantage of using such numerical technique is that a linear system with the constant coefficient matrices is obtained and then the computation becomes easy. In the second step, a system consists of a Stokes problem and a linear elliptic problem is solved. The main results of this article include that (1) Establish the stability of numerical solutions in the time viscosity-splitting method; (2) Provide the convergence results of strongly second order for the velocity and temperature and strongly first order for the pressure. Finally, some numerical results are provided to display the performances of the developed numerical algorithms. |
| Author | Qian, Yanxia Zhang, Tong |
| Author_xml | – sequence: 1 givenname: Tong surname: Zhang fullname: Zhang, Tong email: tzhang@hpu.edu.cn organization: School of Mathematics & Information Science, Henan Polytechnic University, Jiaozuo, 454003, PR China – sequence: 2 givenname: Yanxia surname: Qian fullname: Qian, Yanxia organization: School of Mathematics & Information Science, Henan Polytechnic University, Jiaozuo, 454003, PR China |
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| Cites_doi | 10.1007/s10492-016-0133-y 10.1007/s00220-009-0904-3 10.1108/09615539910297932 10.1090/S0025-5718-1968-0242392-2 10.1016/0362-546X(87)90061-7 10.1002/num.21987 10.1016/j.jmaa.2014.10.037 10.1007/BF01396220 10.1016/j.camwa.2016.07.013 10.1360/N012015-00132 10.1016/j.camwa.2013.11.004 10.1098/rspa.2007.1867 10.1016/j.jmaa.2011.02.020 10.1007/s11075-014-9874-4 10.1093/imanum/drp039 10.1137/110829283 10.11568/kjm.2014.22.4.645 10.1090/S0025-5718-96-00750-8 10.1007/BF00247696 10.1155/2014/726249 10.1137/0719018 10.1016/j.jcp.2014.01.035 10.1007/s10444-014-9353-4 10.1016/j.icheatmasstransfer.2014.12.004 10.1016/j.apnum.2004.02.004 10.1016/j.camwa.2014.06.008 10.1016/j.physd.2015.03.011 10.1016/j.ijheatmasstransfer.2006.05.015 10.1090/S0025-5718-08-02127-3 10.1186/s13661-016-0552-4 10.1137/0729004 10.1088/0951-7715/19/11/006 10.1137/S0036142901385659 |
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| Keywords | Boussinesq system Stability Viscosity-splitting scheme Convergence |
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| SubjectTerms | Boussinesq system Convergence Stability Viscosity-splitting scheme |
| Title | The time viscosity-splitting method for the Boussinesq problem |
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