In this video you can see numerical solutions of the time dependent MHD equations. In the first column on the left you see the solution in a large domain. In order to reduce the numerical cost we want to solve the problem on a smaller domain with suitable boundary conditios on the upper boundary , such that the solution on the smaller domain is close to the solution of the larger domain (first column). In the fourth column (A) we have used absorbing boundary conditions and it turns out that the solution is close to the solution in the larger domain in the first column. In the second (D) and the third column (N) you can see the solutions for Dirichlet and Neumann boundary conditions, respectively. The result is much worse.