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Some results of comparison between numerical and analytic solutions of the one line model for shoreline change

A qualitative understanding of the basic properties of complicated physical phenomena can often be obtained through the study of analytic solutions derived from simplified problems. Analytic solutions of shoreline change model for simple shoreline configurations are derived under idealized wave conditions. | Vietnam Journal of Mechanics, VAST, Vol. 28, No. 2 (2006), pp. 94-102 SOME RESULTS OF COMPARISON BETWEEN NUMERICAL AND ANALYTIC SOLUTIONS OF THE ONE-LINE MODEL FOR SHORELINE CHANGE LE XUAN ROAN Institute of Mechanics, VAST, 264 Doi Can, Hanoi, Vietnam Abstract. A qualitative understanding of the basic properties of complicated physical phenomena can often be obtained through the study of analytic solutions derived from simplified problems. Analytic solutions of shoreline change model for simple shoreline configurations are derived under idealized wave conditions. Both analytic and numerical methods are based on the one-line theory of shoreline change. In this paper some results of comparison of the numerical with analytic solutions are presented. 1. INTRODUCTION Under certain idealized wave conditions and simple shoreline configurations, the equations of one-line theory of shoreline change can be reduced to the one-dimensional equation of heat diffusion type, which in some certain simplified cases can be solved analytically. The analytic solutions are often valuable for giving qualitative insights and investigating the properties of shoreline change. However, it is important to be aware of the limitations of analytic solutions and errors introduced by these limitations. For the real situation, the use of numerical model of shoreline change could be more appropriate. Several authors have presented analytic solutions for certain simplified conditions (e.g. Bakker and Edelman 1965; Bakker 1969; Le Mehaute' and Soldate 1977; Walton and Chiu 1979; Larson, Hanson, and Kraus 1987). In order to describe more realistic situations involving general shoreline configurations, together with time varying wave conditions, ·the one-line theory has been developed using numerical solution techniques (e.g. Price, Tomlinson, and Willis 1973; Sasaki and Sakuramoto 1978; Kraus, Hanson, and Harikai 1985; Hanson and Kraus 1987). Four examples of shoreline evolution for simplified .