Abstract

Purpose This paper aims to propose two parallel two-step finite element algorithms based on fully overlapping domain decomposition for solving the 2D/3D time-dependent natural convection problem. Design/methodology/approach The first-order implicit Euler formula and second-order Crank–Nicolson formula are used to time discretization respectively. Each processor of the algorithms computes a stabilized solution in its own global composite mesh in parallel. These algorithms compute a nonlinear system for the velocity, pressure and temperature based on a lower-order element pair (P1b-P1-P1) and solve a linear approximation based on a higher-order element pair (P2-P1-P2) on the same mesh, which shows that the new algorithms have the same convergence rate as the two-step finite element methods. What is more, the stability analysis of the proposed algorithms is derived. Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms. Findings Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms. Originality/value The novel parallel two-step algorithms for incompressible natural convection problem are proposed. The rigorous analysis of the stability is given for the proposed parallel two-step algorithms. Extensive 2D/3D numerical tests demonstrate that the parallel two-step algorithms can deal with the incompressible natural convection problem for high Rayleigh number well.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call