An augmented source method for the application of nodal equivalence theory

Chang Joo Hah, Purdue University

Abstract

The application of Nodal Equivalence Theory (NET) to advanced nodal methods has required the use of discontinuity factors (DFs) to correct homogenization errors. A conventional way of utilizing DFs in an advanced nodal method has been to apply DFs directly to the nodal matrix equations as multipliers to the group constants. For most problems, the application of DFs has not led to the divergence of the standard numerical iterative method used to solve the multigroup nodal diffusion equations. However, the use of large discontinuity factors resulting from steep flux gradients in the Modular High Temperature Gas Reactor (MHTGR) resulted in the divergence of the iterative methods used for the inner and upscatter iterations. In a physical sense, this problem in the MHTGR represents a break down of a projection system (an iterative method) employed in Nodal Expansion Method (NEM), where the homogenized flux solution in a low order physical space is projected onto a higher order physical space where the reference solution belongs to. The numerical convergence problem does not have a solution within the framework of the existing system of equations represented by Nodal Expansion Method (NEM) and the solution of the problem requires to transform the existing system of equations to another system of equations where the original numerical convergence problem does not exist. In the work performed here, we introduce the Augmented Source Method (ASM) for applying NET to the Nodal Expansion Method (NEM). The ASM transforms the original homogeneous system of equations to an inhomogeneous system of equations, adding an additional external source. External surface sources at a node boundary are introduced to account for the homogenization errors thereby preserving the same matrix properties without DFs which guarantee convergence of iterative techniques. The Augmented Source Method (ASM) produced converged solutions for any magnitude of DFs and reproduced the reference solution when the augmented sources were constructed from the reference quantities. However, the use of an approximate augmented source in the ASM did not provide a consistently improved solution because the accuracy of the ASM solution depends on the determination of an augmented source which requires development of a higher order method for constructing an accurate augmented source. Since the development of a higher order method can not be done within the framework of NEM, the research has been directed to various applications of the ASM using a given reference solution. The application of the ASM to the core depletion calculation demonstrated the use of various approximations for the augmented source. An augmented source which was constant during the burnup cycle resulted in an improved solution in which the eigenvalue error was reduced by a factor of six compared to the nodal solution without DFs.

Degree

Ph.D.

Advisors

Downar, Purdue University.

Subject Area

Engineering|Nuclear physics

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