%0 Journal Article
%T 非定常渗透对流模型一阶分数步长算法的时间误差估计<br>Temporal Error Estimate of First-Order Fractional Step Algorithm for Unsteady Penetrative Convection Model
%A 田耕耘
%J Advances in Applied Mathematics
%P 3039-3051
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/aam.2024.137289
%X 本文研究了求解非定常渗透对流模型的一阶分数步长时间离散算法，该方程是由非定常不可压缩Navier-Stokes方程和热传导方程所耦合的非线性多物理场模型。该算法的优点在于将Navier-Stokes方程的非线性性和不可压缩性进行分离，实现算法的高效性。理论上，在解的正则性假设下，我们得到了速度场和温度场一阶时间收敛阶。最后通过数值算例验证了所得到的收敛性结果。<br />
In this paper, the first-order fractional-step time-discretization algorithm for solving the unsteady penetrative-convection model is studied. This equation is a nonlinear multi-physical model coupled by the unsteady incompressible Navier-Stokes equation and the heat conduction equation. The advantage of the algorithm is that the nonlinearity and incompressibility of the Navier-Stokes equations are separated to realize the high efficiency of the algorithm. Theoretically, under the assumption of the regularity of the solution, we obtain the first-order temporal convergence order of the velocity field and the temperature field. Finally, the convergence results are verified by numerical examples.
%K 非定常渗透对流模型，分数步长法，时间误差估计<br>Unsteady Penetrative Convection Model
%K Fractional Step Algorithm
%K Temporal Error Estimates
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=91169