Defect deferred correction method for two domain natural convection problem

Abstract

This paper concerns defect deferred correction method used to resolve interactions between the atmosphere and ocean for applications like climate research, hurricane modelling and regional weather forecasting. The defect deferred correction method is obtained by combining the defect correction method and the deferred correction method. There are two advantages of using the defect deferred correction method to solve a two domain natural convection problem, namely, reaching the second-order time accuracy and solving small viscosity or diffusion coefficient problems. Finally, we will verify the conclusion from both theoretical analysis and numerical experiments.

Keywords:

• Two domain natural convection
• defect deferred correction
• stability
• convergence
• small parameters

AMS Subject Classification:

• 65M12

Acknowledgments

The authors would like to thank the editor and anonymous reviewers for their helpful comments and suggestions which lead to a considerably improved presentation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the Natural Science Foundation of China (grant number 11861067) and Natural Science Foundation of Xinjiang Uygur Autonomous Region (grant number 2021D01E11).