Stability Analysis of the Quasidiffusion Method on Periodic Heterogeneous 1D Transport Problems

Computational transport methodology based on decomposition of a problem domain into transport and diffusive subdomains

“…Note also that the errors are equal at positions of interfaces between subdomains. However, the solution obtained with asymptotic BCs is more accurate inside the [4,9] 1.3 Â 10 À10 1.7 Â 10 À7 4.9 Â 10 À14 1.1 Â 10 À16 [3,10] 4.4 Â 10 À10 1.6 Â 10 À8 9.6 Â 10 À8 9.7 Â 10 À7 LD [4,9] 1.0 Â 10 À13 3.2 Â 10 À11 1.8 Â 10 À11 1.8 Â 10 À9 transport subdomains. The results also show that the deeper the locations of interfaces are placed in the diffusive region, the closer the numerical solution computed with the domain decomposition is to the original transport solution in the entire domain.…”

“…These results show that two spatial regions have distinct properties from the viewpoint of transport effects. In the left region the values of M E and M E 0 are greater than 10 À3 over a large part of this region (x 2 ½0; 4 [ ½7; 10). The values of M E indicate that there are transport effects.…”

“…To discretize the equations of the QD method, we utilize the SC transport scheme for the transport equation and the secondorder finite-volume method for the LOQD equations [10]. The scalar flux in the right-hand side of the transport equation is approximated by the cell-average scalar flux computed from the LOQD equations.…”

“…Table 2 shows the percentage of cells in the diffusive region in each case. x [3,10], P 1 BCs [4,9], P 1 BCs [3,10], asymptotic BCs [4,9], asymptotic BCs x [3,10], P 1 BCs [4,9], P 1 BCs [3,10], asymptotic BCs [4,9], asymptotic BCs [4,9] 8.9 Â 10 À6 3.9 Â 10 À10 25 [3,10] 1.0 Â 10 À7 1.0 Â 10 À7 35 LD [4,9] 2.4 Â 10 À11 2.4 Â 10 À11 25…”

“…In each particular case, they enable one to evaluate spatial ranges of various kinds of subdomains and areas between them where transport effects are weak but still important. We consider two different transport discretization methods: the QD method that uses the step characteristic (SC) scheme for discretization of the transport equation and a secondorder finite-volume scheme for the LOQD equations [10], the linear discontinuous (LD) finite element method [12].…”