Mechanical Engineering Commons^™

Application Of H-, P- And Hp-Adaptation For Convective Heat Transfer Problems, Xiuling Wang, Darrell W. Pepper

Mechanical Engineering Faculty Research

The purpose of this paper is to describe the development and employment of an hp-adaptive finite element method (FEM) algorithm for solving heat transfer problems in partitioned enclosures, which has attracted the attention of both experimental and theoretical researchers in recent years.

Design/methodology/approach – In the hp-adaptive FEM algorithm presented here, both the element
size and the shape function order are dynamically controlled by an a posteriori error estimator based on the L2 norm; a three-step adaptation strategy is used with a projection algorithm for the flow solver.

Findings – Simulation results are obtained for 2D and 3D natural convection …

Application Of Meshless Methods For Thermal Analysis, Darrell Pepper, Bozidar Sarler

Mechanical Engineering Faculty Research

Many numerical and analytical schemes exist for solving heat transfer problems. The meshless method is a particularly attractive method that is receiving attention in the engineering and scientific modeling communities. The meshless method is simple, accurate, and requires no polygonalisation. In this study, we focus on the application of meshless methods using radial basis functions (RBFs) — which are simple to implement — for thermal problems. Radial basis functions are the natural generalization of univariate polynomial splines to a multivariate setting that work for arbitrary geometry with high dimensions. RBF functions depend only on the distance from some center point. …