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Numerical Stability Verification of a Two-Dimensional Time-Dependent Nonlinear Shallow Water System Using Multidimensional Wave Digital Filtering Network

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Abstract

This paper aims to study the stability effects of a two-dimensional time-dependent nonlinear shallow water (NLSW) system based on the concordance analysis of necessary and sufficient conditions derived from a multidimensional wave digital filtering (MDWDF) network. Approximating the differential equations used to describe elements of a MD passive electrical circuit by grid-based difference equations, the satisfactory Courant–Friedrichs–Levy condition usually known to be necessary are derived with various initial conditions to provide theoretical support for the existence of a MD passive dynamical system and thus stability of the discrete equivalent. Together with the evaluation of the system’s energy and hence solution error propagation that both arise directly and sufficiently to the stability of MDWDF networks, the numerical convergence of the network can be fully established. As a consequence, all instability related aspects in relation to computational errors and overflow corrections are fully excluded leading to uniquely a high degree of robustness of MDWDF architecture. Feasible comparisons are made with a finite element method implemented in the COMSOL Multiphysics to confirm the verification process.

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  1. Department of Information Engineering, Kun Shan University, 949, Da-Wan Road, Yung-Kang Section, Tainan City, Taiwan

    C.-H. Tseng

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Tseng, CH. Numerical Stability Verification of a Two-Dimensional Time-Dependent Nonlinear Shallow Water System Using Multidimensional Wave Digital Filtering Network. Circuits Syst Signal Process 32, 299–319 (2013). https://doi.org/10.1007/s00034-012-9461-7

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  • DOI: https://doi.org/10.1007/s00034-012-9461-7

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