On the accuracy of boundary fitted finite‐difference calculations

Abstract

SUMMARYA description is given of the effects of the discretization of the domain of integration on the accuracy of the results obtained with boundary-fitted finite differences. Three-dimensional unsteady heat conduction problems and two dimensional Navier-Stokes equations are considered. Comparisons with analytic solutions are given for all cases. It is shown that grid shapes influence the accuracy of the results and quantitative error evaluations are provided for some interesting cases.

Simulation of Freezing or Thawing Heat Conduction in Irregular Two-Dimensional Domains by a Boundary-Fitted Grid Method

“…Finite elements needs large computer programs and computer facilities, requiring long processing times. An alternative approach is the boundary-fitted grid method that employs a well behaved transformation in order to generate a nonuniform grid adapted to the irregular domain boundaries (16)(17)(18). This method allows use of a fully conservative numerical scheme like the control volume formulation (19) or subdomain method, which is a variant of the method of weighted residuals.…”

A NUMERICAL METHOD FOR SIMULATING HEAT TRANSFER IN HETEROGENEOUS and IRREGULARLY SHAPED FOODSTUFFS1

“…An alternative approach is the boundary-fitted grid method that employs a well-behaved transformation in order to generate a nonuniform grid adapted to the irregular domain boundaries (Fiora and Ferreri 1978;Ferreri and Ventura 1984;Grandi and Ferreri 1989). This method allows use of a fully conservative numerical scheme like the control volume formulation (Patankar 1980) or subdomain method, which is a variant of the method of weighted residuals.…”