Grid-independent Issue in Numerical Heat Transfer

TL;DR

This paper investigates how grid resolution affects the accuracy of numerical heat transfer simulations, providing a mathematical law and formula to determine the optimal grid density for reliable results.

Contribution

It introduces a mathematical law of grid dependence and a formula to identify the minimum grid density needed for grid-independent, accurate heat transfer simulations.

Findings

Derived a law describing grid dependence in heat transfer simulations.

Presented a formula to determine the minimum grid density for accuracy.

Validated the approach with numerical examples.

Abstract

Grid independent is associated with the accuracy or even rationality of numerical results. This paper takes two-dimensional steady heat transfer for example to reveal the effect of grid resolution on numerical results. The law of grid dependence is obtained and a simple mathematical formula is presented. The production acquired here can be used as the guidance in choosing grid density in numerical simulation and get exact grid independent value without using infinite fine grid. Through analyzing grid independent, we can find the minimum number of grid cells that is needed to get grid-independent results. Such strategy can save computational resource while ensure a rational computational result.