A new second-order consistent splitting scheme for the Natural Convection equations
Abstract
A novel second-order consistent splitting scheme is proposed for the natural convection equations. The scheme is constructed using Taylor expansions about the time level tn+k, where k is a parameter to be determined. It is proved to be stable for all k>4, with the present study focusing primarily on the case k=5. Compared with the conventional splitting scheme based on Taylor expansions about tn+1, the proposed scheme exhibits improved stability. By employing the Sobolev inequality and Gronwall's lemma, we rigorously establish stability of the proposed scheme and derive error estimates in both two and three spatial dimensions. Finally, several numerical experiments are presented to verify the stability and accuracy of the proposed scheme and to demonstrate its effectiveness.
Related
- A second-order linear decoupled scheme with a relaxed zero-energy variable for Rayleigh-Bénard convection
- Energy-Consistent Splitting and Decomposition Approaches for Coupled port-Hamiltonian ODEs
- A Fully Discrete Local Discontinuous Galerkin Method for Quasilinear Stochastic Convection-Diffusion-Type Equations
- Accelerated Convergence of a Second-Order Dynamical System and its Application to Splitting Algorithms for Comonotone Inclusions
- Optimization-based Cell Average Limiters as Metric Projections: Constrained Evolution and Convergence Analysis for Convection-diffusion Equations
BibTeX
@misc{si2026secondorder,
title = {{A new second-order consistent splitting scheme for the Natural Convection equations}},
author = {Zhiyong Si and Yimei Ma and Yunxia Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28961},
eprint = {2609.28961},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28961},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A new second-order consistent splitting scheme for the Natural Convection equations
AU - Zhiyong Si
AU - Yimei Ma
AU - Yunxia Wang
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.28961
UR - https://arxiv.org/abs/2609.28961
AB - A novel second-order consistent splitting scheme is proposed for the natural convection equations. The scheme is constructed using Taylor expansions about the time level t^n+k, where k is a parameter to be determined. It is proved to be stable for all k>4, with the present study focusing primarily on the case k=5. Compared with the conventional splitting scheme based on Taylor expansions about t^n+1, the proposed scheme exhibits improved stability. By employing the Sobolev inequality and Gronwall's lemma, we rigorously establish stability of the proposed scheme and derive error estimates in both two and three spatial dimensions. Finally, several numerical experiments are presented to verify the stability and accuracy of the proposed scheme and to demonstrate its effectiveness.
ER -