Boundary Conditions for Conservation Laws in 2-D

Scalar conservation laws have earlier been prescribed with three different boundary conditions -- absorbing boundaries (or no condition), periodic conditions, and Dirichlet conditions.

We introduce a new kind of boundary conditions for scalar conservation laws, the zero flux boundary condition; that is, we require the flux to be zero in the normal at the boundary.

As a means of analysis for such equations, we can use front tracking combined with dimesional splitting in multidimensions. For more details see Karlsen, Lie, and Risebro [1]

In the figure below, we show an example that includes absorbing, Dirichlet and zero flux boundary conditions. The condition at the left boundary gives a strong shock that reflects from the lower wall and forms a triple-shock point. The leading shock then diffracts around the corner (lower left plot) before it is reflected by the right wall (lower right plot). A MPEG-movie of this example is available.

We also provide a MPEG-movie of an oblique shock that interacts with 90 degree corner of a solid wall.