Abstract The computational efficiencies of two nodal integral methods for the numerical solution of linear convection-diffusion equations are studied. Although the first, which leads to a second-order spatial truncation error, has been reported earlier, it is reviewed in order to lead logically to the development here of the second, which has a third-order error. This third-order nodal integral method is developed by introducing an upwind approximation for the linear terms in the “pseudo-sources” that appear in the transverse-averaged equations introduced in the formulation of nodal integral methods. This upwind approximation obviates the need to develop and solve additional equations for the transverse-averaged first moments of the unknown, as would have to be done in a more straightforwardly developed higher-order nodal integral method. The computational efficiencies of the second-order nodal method and the third-order nodal method—of which there are two versions: one, a full third-order method and the other, which uses simpler second-order equations near the boundaries—are compared with those of both a very traditional method and a recently developed state-of-the-art method. Based on the comparisons reported here for a challenging recirculating flow benchmark problem it appears that, among the five methods studied, the second-order nodal integral method has the highest computational efficiency (the lowest CPU computing times for the same accuracy requirements) in the practical 1% error regime.
[1]
Conservative versions of the locally exact consistent upwind scheme of second order (Lecusso-scheme)
,
1992
.
[2]
A. Ougouag,et al.
ILLICO-HO: A Self-Consistent Higher Order Coarse-Mesh Nodal Method
,
1988
.
[3]
Albert J. Valocchi,et al.
The Cell Analytical‐Numerical Method for Solution of the Advection‐Dispersion Equation: Two‐Dimensional Problems
,
1990
.
[4]
M. Israeli,et al.
Efficiency of Navier-Stokes Solvers
,
1977
.
[5]
R. A. Shober.
A Nodal Method for Solving Transient Fewgroup Neutron Diffusion Equations
,
1978
.
[6]
R. Witt,et al.
An Upwind Nodal Integral Method for Incompressible Fluid Flow
,
1993
.
[7]
A. G. Hutton,et al.
THE NUMERICAL TREATMENT OF ADVECTION: A PERFORMANCE COMPARISON OF CURRENT METHODS
,
1982
.
[8]
B. P. Leonard.
The QUICK algorithm - A uniformly third-order finite-difference method for highly convective flows
,
1980
.
[9]
J. J. Dorning,et al.
Nodal Green's function method for multidimensional neutron diffusion calculations
,
1978
.
[10]
W. C Horak,et al.
A nodal coarse-mesh method for the efficient numerical solution of laminar flow problems
,
1981
.
[11]
R. Agarwal.
A third-order-accurate upwind scheme for Navier-Stokes solutions in three dimensions
,
1981
.