B.A.V. Bennett,

Numerical Heat Transfer, Part B, 52, 1–32, 2007

Abstract

The local rectangular refinement (LRR) solution-adaptive gridding method, developed a decade ago to solve coupled nonlinear elliptic partial differential equations in two dimensions (2D), has been extended to three dimensions (3D). Like LRR2D, LRR3D automatically generates orthogonal unstructured adaptive grids, discretizes governing equations using multiple-scale finite differences, and solves the discretized system at all points simultaneously using Newton's method. The computational/programming challenges overcome in developing LRR3D are described. Next, a 3D convection-diffusion-reaction problem with a known solution is used to demonstrate the accuracy and efficiency of LRR3D versus a Newton solver on a structured grid. Finally, natural convection within a tilted differentially heated cubic cavity with perfectly conducting nonisothermal walls is examined for a range of Rayleigh numbers (10³ to 4×10⁴) and for two inclinations (45° and 90°) of the isothermal walls. Excellent agreement with published computational and experimental results is observed.