An efficient fully decoupled finite element method with second-order accuracy for the micropolar Rayleigh-Benard convection system

TL;DR

This paper introduces a fully decoupled, second-order accurate finite element method for simulating the complex micropolar Rayleigh-Benard convection system, significantly simplifying computations while maintaining high accuracy.

Contribution

A novel linear, fully decoupled, second-order time-accurate finite element method for the micropolar Rayleigh-Benard system, with rigorous stability and error analysis.

Findings

Method achieves second-order accuracy in time.

Numerical tests confirm stability and effectiveness.

Simplifies computations by solving fewer elliptic problems.

Abstract

The micropolar Rayleigh-B{\'e}nard convection system, which consists of Navier-Stokes equations, the angular momentum equation, and the heat equation, is a strongly nonlinear, coupled, and saddle point structural multiphysics system. A second-order pressure projection finite element method, which is linear, fully decoupled, and second-order accurate in time, is proposed to simulate the system. Only a few decoupled linear elliptic problems with constant coefficients are solved at each time step, simplifying calculations significantly. The stability analysis of the method is established and the optimal error estimates are derived rigorously with the negative norm technique. Extensive numerical simulations, including 2D and 3D accuracy tests, the lid-driven cavity flow, and the passive-scalar mixing experiment, are carried out to illustrate the effectiveness of the method.