
54 Modeling shallow water ows using the DG method
4.2.2 Formulation of TVD slope limiters
As shown in Section 4.1, the high-order schemes suffer from spurious
oscillations in the vicinity of discontinuities and strong gradients. The
idea of a slope limiter is to reconstruct the variables with limited slopes
using neighboring elements. The data reconstruction method is based
on the monotonic upstream scheme for conservation laws (MUSCL)
(van Leer, 1979) and the piecewise parabolic method (PPM) (Colella and
Woodward, 1984).
The limiting process is applied after the unknowns are calculated
in every element in the computational domain. Followi