A linear stability analysis of the cell-wise relaxation implicit discontinuous Galerkin method proposed in our previous work was carried out for a scalar advection equation using three different generating patterns of triangular cells in two-dimensional space. A detailed mathematical formulation of the stability analysis is presented in this paper. It is shown that the present cell-wise implicit method with spatial accuracies up to fourth order is stable with very large Courant-Friedrichs-Lewy (CFL) numbers.
ASJC Scopus subject areas
- Mechanical Engineering
- Physics and Astronomy(all)
- Fluid Flow and Transfer Processes