ITERATIVE SOLUTION OF FLUID FLOW IN FINNED TUBES

Abstract

A difference-based numerical algorithm is developed to efficiently solve a class of elliptic boundary value problems up to any desired order of accuracy. Through multi-level discretization the algorithm uses the multigridconcept of nested iterations to accelerate the convergence rate at higher discretization levels and exploits the advantages of extrapolation methods to achieve higher order accuracy with less computational work. The algorithm employs the SOR method to solve the discrete problem at each discretization level by using an estimated optimum value of the relaxation parameter. The advantages of the algorithm are shown through comparison with the simple discrete method for simulations of fluid flows in finned circular ducts.