Abstract
In this paper, we give a modified characteristics projection finite element method for the time-dependent conduction-convection problems, which is gotten by combining the modified characteristics finite element method and the projection method. The stability and the error analysis shows that our method is stable and has optimal convergence order. In order to show the effect of our method, some numerical results are presented. From the numerical results, we can see that the modified characteristics projection finite element method can simulate the fluid field, temperature field, and pressure field very well.
Highlights
1 Introduction The conduction-convection problem constitutes an important system of equations in atmospheric dynamics and dissipative nonlinear system of equations
There is a significant amount of literature as regards this problem
The projection methods, which are efficient methods for solving the incompressible time-dependent fluid flow, were first introduced by Chorin [ ] and Temam [ ] in the late s. This method is based on a special time-discretization of the Navier-Stokes equations
Summary
The conduction-convection problem constitutes an important system of equations in atmospheric dynamics and dissipative nonlinear system of equations. The projection methods, which are efficient methods for solving the incompressible time-dependent fluid flow, were first introduced by Chorin [ ] and Temam [ ] in the late s This method is based on a special time-discretization of the Navier-Stokes equations. A second order MMOC mixed defect-correction finite element method [ ] for time-dependent Navier-Stokes problems was given. Notsu et al gave a single-step characteristics finite difference analysis for the convection-diffusion problems [ ] and a single-step finite element method for the incompressible Navier-Stokes equations [ ]. We consider the time-dependent conduction-convection problem in two dimensions whose coupled equations governing viscous incompressible flow and heat transfer for the incompressible fluid are Boussinesq approximations to the Navier-Stokes equations.
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