From 660a8677c9748d0e6cde4c528d56bce00d4b3ab4 Mon Sep 17 00:00:00 2001 From: David Wells Date: Mon, 6 May 2019 19:15:12 -0400 Subject: [PATCH] step-28: minor typography fixes 1. Fix the link to the paper 2. Fix some odd link titles that cannot handle mathjax formatting 3. Other minor typography fixes --- examples/step-28/doc/intro.dox | 30 +++++++++++++----------------- examples/step-28/doc/results.dox | 2 +- 2 files changed, 14 insertions(+), 18 deletions(-) diff --git a/examples/step-28/doc/intro.dox b/examples/step-28/doc/intro.dox index cd8506b765..7bc75a176e 100644 --- a/examples/step-28/doc/intro.dox +++ b/examples/step-28/doc/intro.dox @@ -2,32 +2,28 @@ This program was contributed by Yaqi Wang and Wolfgang Bangerth. Results from this program are used and discussed in the publication -"Three-dimensional $h$-adaptivity for the multigroup neutron diffusion +"Three-dimensional h-adaptivity for the multigroup neutron diffusion equations" by Yaqi Wang, Wolfgang Bangerth and Jean Ragusa. The paper's full bibliographic details are as follows: @code @Article{WBR09, - author = {Yaqi Wang and Wolfgang Bangerth and Jean Ragusa}, - title = {Three-dimensional $h$-adaptivity for the multigroup - neutron diffusion equations}, - journal = {Progr. Nucl. Energy}, - year = 2009, - volume = 51, - pages = {543--555} + author = {Yaqi Wang and Wolfgang Bangerth and Jean Ragusa}, + title = {Three-dimensional h-adaptivity for the multigroup + neutron diffusion equations}, + journal = {Progr. Nucl. Energy}, + year = 2009, + volume = 51, + pages = {543--555} } @endcode -A preprint that mostly matches the final version of the paper is -available here. +The paper is available here.

Introduction

- - - In this example, we intend to solve the multigroup diffusion approximation of the neutron transport equation. Essentially, the way to view this is as follows: In a nuclear reactor, neutrons are speeding around at different energies, get @@ -176,7 +172,7 @@ one for stable operation of a reactor: if it is less than one, the chain reactio die down, whereas nuclear bombs for example have a $k$-eigenvalue larger than one. A stable reactor should have $k_{\mathrm{eff}}=1$. -[For those who wonder how this can be achieved in practice without +For those who wonder how this can be achieved in practice without inadvertently getting slightly larger than one and triggering a nuclear bomb: first, fission processes happen on different time scales. While most neutrons are released very quickly after a fission event, a small number of neutrons @@ -201,7 +197,7 @@ Finally, some of the absorption and scattering reactions have some stability built in; for example, higher neutron fluxes result in locally higher temperatures, which lowers the density of water and therefore reduces the number of scatterers that are necessary to moderate neutrons from high to -low energies before they can start fission events themselves.] +low energies before they can start fission events themselves. In this tutorial program, we solve above $k$-eigenvalue problem for two energy groups, and we are looking for the largest multiplication factor @@ -586,7 +582,7 @@ This whole arrangement would make the description or spatially dependent material parameters very complicated. It will not become much simpler, but we will make one approximation: we merge the volume inhabited by each cylindrical rod and the surrounding water into volumes of quadratic cross section into -so-called ``pin cells'' for which homogenized material data are obtained with +so-called `pin cells' for which homogenized material data are obtained with nuclear database and knowledge of neutron spectrum. The homogenization makes all material data piecewise constant on the solution domain for a reactor with fresh fuel. Spatially dependent material parameters are then looked up for the diff --git a/examples/step-28/doc/results.dox b/examples/step-28/doc/results.dox index d4b55f9586..b8507db056 100644 --- a/examples/step-28/doc/results.dox +++ b/examples/step-28/doc/results.dox @@ -89,7 +89,7 @@ Then we plot the convergence data with polynomial order being equal to 1,2 and 3 -The estimated ``exact'' k-effective = 0.906834721253 which is simply from last +The estimated `exact' k-effective = 0.906834721253 which is simply from last mesh iteration of polynomial order 3 minus 2e-10. We see that h-adaptive calculations deliver an algebraic convergence. And the higher polynomial order is, the faster mesh iteration converges. In our problem, we need smaller number of DoFs to achieve same -- 2.39.5