Numerical Stability Verification of the Nonlinear Shallow Water System using Multidimensional Wave Digital Filtering Network

This paper studies necessary and sufficient conditions for numerical stability verification of a twodimensional time-dependent nonlinear shallow water (NLSW) system integrated by multidimensional wave digital filtering (MDWDF) network. As the verification activities are directly linked to the passivity of the system, the proposed solutions from the MDWDF network are intensively analyzed for their convergent behaviors based on the system's energy evaluation known to be sufficient condition. Together with the satisfactory of Courant-Friedrichs-Levy (CFL) bound (known to be necessary condition), which guarantees existence of a MD passive system and thus stability of the discrete equivalent, the verification process has led to uniquely a high degree of robustness of MDWDF architecture with focusing on the handling of computational error. As a result, all key aspects including properties of MD passivity and numerical stability can widely be kept under control. Keyword: NLSW, MDWDF network, stability, passivity.