<p>In this paper, we propose a new second-order variable stepsize time-filtering algorithm for simulating natural convection phenomena. Unlike existing methods, which are primarily confined to constant stepsize frameworks, the proposed algorithm introduces a variable stepsize scheme characterized by simple implementation, high computational efficiency, and superior convergence accuracy. Furthermore, to address the practical requirements of low-memory solvers, the algorithm is extended to an adaptive variable stepsize and variable order framework for fluid flow simulations. The key theoretical contribution lies in the rigorous proof of the algorithm’s unconditional stability and second-order convergence under variable stepsize conditions. This analysis resolves a critical limitation of conventional constant stepsize methods–their inherent inflexibility in handling multiscale temporal dynamics and complex flow regimes. By leveraging adaptive stepsize control, our method not only overcomes the theoretical constraints of constant stepsize approaches but also ensures robust performance in scenarios involving sharp gradients or transient behaviors. Finally, the effectiveness and computational efficiency of the algorithm are validated through numerical experiments.</p>