Comparison of three approximations to the linear-linear nodal transport method in weighted diamond-difference form

Journal Article · Tue Nov 01 00:00:00 EST 1988 · Nucl. Sci. Eng.; (United States)

DOI:https://doi.org/10.13182/NSE88-5· OSTI ID:6307116

Azmy, Y Y

Two previously derived approximations to the linear-linear nodal transport method, the linear-nodal (LN) and the linear-linear (LL) methods, are reexamined, together with a new approximation, the bilinear (BL) method, that takes into account the bilinear nodal flux moment. The three methods differ in the degree of analyticity retained in the final discrete variable equations; however, they all possess the very high accuracy characteristic of nodal methods. Unlike previous work, the final equations are manipulated and cast in the form of the classical weighted diamond-difference (WDD) equations (not just a WDD algorithm). This makes them simple to implement in a computer code, especially for those users who have experience with WDD algorithms. Other algorithms, such as the nodal algorithm, also can be used to solve the WDD-form equations. A computer program that solves two-dimensional transport problems using the LN, LL, or the BL method is used to solve three test problems. The results are used to confirm our algebraic manipulations of the nodal equations and also to compare the performance of the three methods from the computational, as well as the theoretical, point of view. The three methods are found to have comparable accuracies for the problems studies, especially on meshes that are sufficiently fine.

• Research Organization: Oak Ridge National Lab., Engineering Physics and Mathematics Div., Oak Ridge, TN (US)
• OSTI ID: 6307116
• Journal Information: Nucl. Sci. Eng.; (United States), Vol. 100:3
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
COMPUTER CODES
ALGORITHMS
RADIATION TRANSPORT
ACCURACY
ANALYTICAL SOLUTION
CALCULATION METHODS
COMPUTER CALCULATIONS
EQUATIONS
TWO-DIMENSIONAL CALCULATIONS
MATHEMATICAL LOGIC
220100* - Nuclear Reactor Technology- Theory & Calculation
220400 - Nuclear Reactor Technology- Control Systems