These html pages are based on the PhD thesis "Cluster-Based Parallelization of Simulations on Dynamically Adaptive Grids and Dynamic Resource Management" by Martin Schreiber.

There is also more information and a PDF version available.

There is also more information and a PDF version available.

Working with triangles, a straightforward evaluation of the term F(U_{i}(t)) ⋅(x,y) involving both flux
functions G(U) and H(U) followed by a multiplication with the outward pointing normal can be
optimized. We use the so-called rotational invariancy [Tor01], with flux functions for the hyperbolic
systems considered in this thesis holding a crucial property.

We consider a two-dimensional normal vector _{e} = (cos(α),sin(α))^{T } pointing outward the edge e.
Then, for the computation of the flux update, the equation

| (2.13) |

holds true for a given rotation matrix R(α). The matrix is setup with an n-dimensional rotation
matrix with the entries stored to the n×n direction dependent components such as the velocity and
momentums and 1 on the diagonal for direction independent components. This matrix rotates, e.g.,
orientation-dependent components such as the velocity and momentum which are parallel to _{e} to the
x-axis (see Appendix A.1.7 for an example).

For later purpose, the right hand side of Equation (2.13) is further described:

- 1.
- To compute the flux across an edge, the conserved quantities depending on a direction are first rotated from the reference space to the so-called edge space [AS98].
- 2.
- Then, the change of conserved quantities is evaluated in the one-dimensional edge space.
- 3.
- Finally, the updates related to the flux are rotated back to reference space and applied to the conserved quantities stored in the reference space.