From 8a85eb9ee1344edd2706fd97ae47de20a111e4d8 Mon Sep 17 00:00:00 2001 From: David Schneider Date: Wed, 16 Dec 2020 14:56:23 +0100 Subject: [PATCH] Fix README typos --- coupled_laplace_problem/README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/coupled_laplace_problem/README.md b/coupled_laplace_problem/README.md index 0f60b76..e9fbc10 100644 --- a/coupled_laplace_problem/README.md +++ b/coupled_laplace_problem/README.md @@ -2,14 +2,14 @@ Laplace equation coupled to an external simulation program ------------------------------------------ ## Overview -preCICE allows to couple deal.II to external simulation software, such as OpenFOAM, SU2, or CalculiX. To keep dependencies of this example minimal, we couple deal.II to an external C++ program, which provides a time varying boundary condition. The deal.II code consists mainly of the [`step-4` tutorial program](https://www.dealii.org/developer/doxygen/deal.II/step_4.html), where a simple Laplace problem is solved. +preCICE allows to couple deal.II to external simulation software, such as OpenFOAM, SU2, or CalculiX. To keep dependencies of this example minimal, we couple deal.II to an external C++ program, which provides a time varying boundary condition. The deal.II code consists mainly of the step-4 tutorial program, where a simple Laplace problem is solved. Coupling with preCICE is usually carried out along surfaces in order to apply a Dirichlet-Neumann coupling between two domains (volume coupling is also possible). For the sake of simplicity, we couple here an external C++ program in a unidirectional fashion to one side of our quadrilateral domain. The external C++ program generates a parabolic boundary profile with time varying amplitude. The boundary values are then used in the Laplace solver as a Dirichlet boundary condition. ## Time discretization Coupled simulations deal mostly with time-dependent problems. Hence, we make the stationary Laplace problem from step-4 time dependent. @f{align*} - \\frac{\partial u}{\partial t}-\Delta u &= f \qquad\qquad & \text{in}\ \Omega, + \frac{\partial u}{\partial t}-\Delta u &= f \qquad\qquad & \text{in}\ \Omega, \\ u &= x^2+y^2 \qquad\qquad & \text{on}\ \partial\Omega_s, \\ @@ -19,7 +19,7 @@ with the fixed Dirichlet boundary \Omega_s, the coupling boundary \Omega_c and t The system is consequently discretized by a first-order backward Euler method, resulting in @f{align*} - \\frac{u^{n+1}-u^n}{\Delta t}-\Delta u^{n+1} &= f \qquad\qquad & \text{in}\ \Omega, + \frac{u^{n+1}-u^n}{\Delta t}-\Delta u^{n+1} &= f \qquad\qquad & \text{in}\ \Omega, @f} at the next time level n+1. -- 2.39.5