The discontinuous Galerkin (DG) method is combined with the spectral
deferred correction (SDC) time integration approach to solve the fluid dynamic
equations. The moment limiter is generalized for nonuniform grids with hanging
nodes that result from adaptive mesh refinement. The effect of characteristic,
primitive, or conservative decomposition in the limiting stage is studied. In
general, primitive variable decomposition is a better option, especially in two
and three dimensions. The accuracy-preserving total variation diminishing
(AP-TVD) marker for troubled-cell detection, which uses an averaged-derivative
basis, is modified to use the Legendre polynomial basis. Given that the latest
basis is generally used for DG, the new approach avoids transforming to
the averaged-derivative basis, what results in a more efficient technique.
Further, a new error estimator is proposed to determine where to refine or
coarsen the grid. This estimator is compared against other estimator used
in the literature and shows an improved performance. Canonical tests in
one, two, and three dimensions are conducted to show the accuracy of the
solver.