From: Timo Heister Date: Thu, 27 Jul 2017 18:17:14 +0000 (-0400) Subject: improve documentation of Functions::StokesLSingularity X-Git-Tag: v9.0.0-rc1~1379^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F4671%2Fhead;p=dealii.git improve documentation of Functions::StokesLSingularity --- diff --git a/include/deal.II/base/flow_function.h b/include/deal.II/base/flow_function.h index fe47d66194..660089bb65 100644 --- a/include/deal.II/base/flow_function.h +++ b/include/deal.II/base/flow_function.h @@ -205,7 +205,16 @@ namespace Functions /** - * The solution to Stokes' equations on an L-shaped domain. + * A singular solution to Stokes' equations on a 2d L-shaped domain. + * + * This function satisfies $-\triangle \mathbf{u} + \nabla p = 0$ and + * represents a typical singular solution around a reentrant corner of an + * L-shaped domain that can be created using GridGenerator::hyper_L(). The + * velocity vanishes on the two faces of the re-entrant corner and + * $\nabla\mathbf{u}$ and $p$ are singular at the origin while they are + * smooth in the rest of the domain because they can be written as a product + * of a smooth function and the term $r^{\lambda-1}$ where $r$ is the radius + * and $\lambda \approx 0.54448$ is a fixed parameter. * * Taken from Houston, Schötzau, Wihler, proceeding ENUMATH 2003. * @@ -235,9 +244,10 @@ namespace Functions double Psi_3(double phi) const; /// The 4th derivative of Psi() double Psi_4(double phi) const; - /// The angle of the reentrant corner + /// The angle of the reentrant corner, set to 3*pi/2 const double omega; - /// The exponent of the radius + /// The exponent of the radius, computed as the solution to + /// $\sin(\lambda\omega)+\lambda*sin(\omega)=0$ static const double lambda; /// Cosine of lambda times omega const double coslo;