An Adaptive Time Filter Based Finite Element Method for the Velocity-Vorticity-Temperature Model of the Incompressible Non-Isothermal Fluid Flows

This paper studies a velocity-vorticity-temperature (VVT) model of the Boussinesq equations and introduces a numerical method for solving that. The proposed numerical method adds separate three minimally intrusive steps, one for each fluid variable, except pressure, to the standard semi-implicit backward-Euler (BE) approximation of VVT-model. The key idea in these intrusive steps is to post-process the BE approximate solutions with 2-step, second order, linear time filters. The paper provides full mathematical analysis of the proposed numerical method, and two numerical experiments for that. The first numerical experiment verifies the predicted convergence rates while the second one shows the effectiveness of the method on a benchmark problem.

Keywords:

Finite element method, The Boussinesq equations Time filter,

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