I am trying to solve shallow water equations using DG methods. Flow over a bump is a common problem that comes up in this context. For example (http://loki.udc.es/info/asignaturas/calculo_ii/Finite%20Volumes%20IMWE.pdf, page 46). These are my questions:
- The boundary conditions are mentioned only for the upstream discharge and downstream height. How can I get the boundary values for upstream height and downstream discharge that is required for flux calculations?
- How can I apply slope limiters at the boundaries in this case or even a simpler case of an advection equation where Dirichlet boundary condition is specified at the boundary?