The Relationship between the Coarse-Mesh Finite Difference and the Coarse-Mesh Diffusion Synthetic Acceleration Methods

2014 ◽  
Vol 178 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Edward W. Larsen ◽  
Blake W. Kelley
Keyword(s):  
Finite Difference ◽  
Coarse Mesh ◽  
Diffusion Synthetic Acceleration ◽  
Acceleration Methods ◽  
The Relationship

scholarly journals MULTILEVEL CMFD ACCELERATION METHODS FOR WHOLE CORE REACTOR SIMULATION IN VERA

2021 ◽  
Vol 247 ◽  
pp. 02037
Author(s):  
Luke Cornejo ◽  
Benjamin Collins ◽  
Shane Stimpson
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Virtual Environment ◽  
Difference Method ◽  
Neutron Transport ◽  
Coarse Mesh ◽  
Reactor Physics ◽  
Acceleration Methods ◽  
Solver Performance ◽  
Full Core

Ongoing efforts are being made to improve the performance of MPACT as the deterministic neutron transport solver in the Virtual Environment for Reactor Analysis (VERA). As other parts of the code have been improved, the coarse mesh finite difference method (CMFD) has come to take up a significant portion of the runtime. Multilevel-in-energy CMFD and multilevel-in-space CMFD solvers have been used to improve CMFD solver performance. A new multilevel-in-space-and-energy CMFD solver is being introduced that combines components of these two methods. W-Cycles and partial W-Cycles are being investigated to further improve the efficiency of the multilevel-in-energy CMFD solver. The performance of these methods is demonstrated on full core reactor physics problems of interest to VERA.

Controlling Numerical Dispersion by Variably Timed Flux Updating in Two Dimensions

1982 ◽  
Vol 22 (03) ◽  
pp. 409-419 ◽  
Author(s):  
R.G. Larson
Keyword(s):  
Finite Difference ◽  
Pressure Gradient ◽  
Single Point ◽  
Companion Paper ◽  
Two Dimensions ◽  
Independent Component ◽  
Numerical Dispersion ◽  
Coarse Mesh ◽  
Fixed Concentration ◽  
Order Of Magnitude

Abstract The variably-timed flux updating (VTU) finite difference technique is extended to two dimensions. VTU simulations of miscible floods on a repeated five-spot pattern are compared with exact solutions and with solutions obtained by front tracking. It is found that for neutral and favorable mobility ratios. VTU gives accurate results even on a coarse mesh and reduces numerical dispersion by a factor of 10 or more over the level generated by conventional single-point (SP) upstream weighting. For highly unfavorable mobility ratios, VTU reduces numerical dispersion. but on a coarse mesh the simulation is nevertheless inaccurate because of the inherent inadequacy of the finite-difference estimation of the flow field. Introduction A companion paper (see Pages 399-408) introduced the one-dimensional version of VTU for controlling numerical dispersion in finite-difference simulation of displacements in porous media. For linear and nonlinear, one- and two-independent-component problems, VTU resulted in more than an order-of-magnitude reduction in numerical dispersion over conventional explicit. SP upstream-weighted simulations with the same number of gridblocks. In this paper, the technique is extended to two dimensional (2D) problems, which require solution of a set of coupled partial differential equations that express conservation of material components-i.e., (1) and (2) Fi, the fractional flux of component i, is a function of the set of s - 1 independent-component fractional concentrations {Ci}, which prevail at the given position and time., the dispersion flux, is given by an expression that is linear in the specie concentration gradients. The velocity, is proportional to the pressure gradient,. (3) where lambda, in general, can be a function of composition and of the magnitude of the pressure gradient. The premises on which Eqs. 1 through 3 rest are stated in the companion paper. VTU in Two Dimensions The basic idea of variably-timed flux updating is to use finite-difference discretization of time and space, but to update the flux of a component not every timestep, but with a frequency determined by the corresponding concentration velocity -i.e., the velocity of propagation of fixed concentration of that component. The concentration velocity is a function of time and position. In the formulation described here, the convected flux is upstream-weighted, and all variables except pressure are evaluated explicitly. As described in the companion paper (SPE 8027), the crux of the method is the estimation of the number of timesteps required for a fixed concentration to traverse from an inflow to an outflow face of a gridblock. This task is simpler in one dimension, where there is only one inflow and one outflow face per gridblock, than it is in two dimensions, where each gridblock has in general multiple inflow and outflow faces. SPEJ P. 409^

scholarly journals Analytic Coarse-Mesh Finite-Difference Method Generalized for Heterogeneous Multidimensional Two-Group Diffusion Calculations

2003 ◽  
Vol 144 (1) ◽  
pp. 23-35 ◽  
Author(s):  
Nuria García-Herranz ◽  
Oscar Cabellos ◽  
José M. Aragonés ◽  
Carol Ahnert
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Coarse Mesh

A Pin Power Reconstruction Method for CANDU Reactor Cores Based on Coarse-Mesh Finite Difference Calculations

2000 ◽  
Vol 130 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Hyung-Seok Lee ◽  
Won Sik Yang ◽  
Man Gyun Na ◽  
Hangbok Choi
Keyword(s):  
Finite Difference ◽  
Reconstruction Method ◽  
Coarse Mesh ◽  
Reactor Cores
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