Using Hough Harmonics to Validate and Assess Nonlinear shallow-Water Models

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  • 1 Department of Mathematics, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ. CEP22453, Brazil
  • | 2 Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139
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Abstract

The implementation of a technique for locating programming errors in shallow-water codes, establishing the correctness of the code, and assessing the performance of the numerical model under various flow conditions is described. The right-hand side of the differential equations is modified in such a way that the exact solution of the nonlinear initial-value problem is known, so that the truncation error of the numerical scheme can be studied in detail. The exact solution is prescribed to be any linear combination of Hough harmonies which propagate in time according to their natural frequencies.

Abstract

The implementation of a technique for locating programming errors in shallow-water codes, establishing the correctness of the code, and assessing the performance of the numerical model under various flow conditions is described. The right-hand side of the differential equations is modified in such a way that the exact solution of the nonlinear initial-value problem is known, so that the truncation error of the numerical scheme can be studied in detail. The exact solution is prescribed to be any linear combination of Hough harmonies which propagate in time according to their natural frequencies.

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