bstract: In this seminar, we propose to use overset grids to capture
shocks that occur in the solutions of hyperbolic conservation laws. For
higher order schemes, limiters are used near solution discontinuities. For
discontinuous Galerkin method, a troubled cell indicator is used to locate
the discontinuity and a limiter is applied in the identified locations. The
use of limiter in zones where limiting is not needed reduces the order of
the scheme in those locations. Weighted Essentially Non Oscillatory (WENO)
limiters address this issue. We present a WENO limiting strategy using only
the immediate neighbors. To reduce the workload of the troubled cell
indicator and the limiter, we isolate the zones where limiting is needed
and use overset grids in those locations. To do this, we use a
discontinuous Galerkin solver with a coarse grid to get the troubled cell
data that is used to determine the approximate location of the shock. An
overset grid aligned to the shock is constructed based on this information.
We run the solver again with the coarse grid solution as the initial
condition with limiting occurring only in the overset grid to give a
solution with the shock aligned to the grid line. We validate this method
using a standard test case and present results for supersonic flow over a
circular cylinder. For the flow over a circular cylinder, the results
obtained are validated using an existing analytical method for calculating
the shock offset distance.​