On a Simple and Effective Thermal Open Boundary Condition for Convective Heat Transfer Problems

TL;DR

This paper introduces a simple, energy-stable thermal open boundary condition for convective heat transfer problems that effectively handles complex flow regimes with vortices and backflows, ensuring numerical stability and accuracy.

Contribution

The paper proposes a novel, energy-stable thermal open boundary condition that is easy to implement and effective in complex flow scenarios, improving upon previous methods.

Findings

The boundary condition maintains energy stability in simulations.

It effectively handles vortices and backflows at open boundaries.

Numerical results show improved accuracy over previous methods.

Abstract

We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary will not cause an ``energy-like'' temperature functional to increase over time, irrespective of the state of flow on the open boundary. It is effective in coping with thermal open boundaries even in flow regimes where strong vortices or backflows are prevalent on such boundaries, and it is straightforward to implement. Extensive numerical simulations are presented to demonstrate the stability and effectiveness of our method for heat transfer problems with strong vortices and backflows occurring on the open boundaries. Simulation results are compared with previous works to demonstrate the accuracy of the presented method.