
27Chapter two: General formulation of the discontinuous Galerkin method
shown in Equation (2.79). In addition, it should preserve conservation
across discontinuities by fullling the condition given by Equation (2.80).
Last, the eigenvectors of
must be linearly independent.
===
AU UUAU
LR
(2.79)
×()–( )(
FU FU =A
RL
(2.80)
2.6 Time integration
Since the discontinuous Galerkin method is a local formulation, the
explicit time integration is preferred. The implicit time integration will
result in a global matrix, which breaks the local formulation. For problems
involving shock waves, the total variation diminishing (TVD) Runge–
Kutt ...