SUMMARYA hybrid scheme composed of ÿnite-volume and ÿnite-di erence methods is introduced for the solution of the Boussinesq equations. While the ÿnite-volume method with a Riemann solver is applied to the conservative part of the equations, the higher-order Boussinesq terms are discretized using the ÿnite-di erence scheme. Fourth-order accuracy in space for the ÿnite-volume solution is achieved using the MUSCL-TVD scheme. Within this, four limiters have been tested, of which van-Leer limiter is found to be the most suitable. The Adams-Basforth third-order predictor and Adams-Moulton fourth-order corrector methods are used to obtain fourth-order accuracy in time. A recently introduced surface gradient technique is employed for the treatment of the bottom slope. A new model 'HYWAVE', based on this hybrid solution, has been applied to a number of wave propagation examples, most of which are taken from previous studies. Examples include sinusoidal waves and bi-chromatic wave propagation in deep water, sinusoidal wave propagation in shallow water and sinusoidal wave propagation from deep to shallow water demonstrating the linear shoaling properties of the model. Finally, sinusoidal wave propagation over a bar is simulated. The results are in good agreement with the theoretical expectations and published experimental results.

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SUMMARYNumerical methods have become well established as tools for solving problems in hydraulic engineering. In recent years the ÿnite volume method (FVM) with shock capturing capabilities has come to the fore because of its suitability for modelling a variety of types of ow; subcritical and supercritical; steady and unsteady; continuous and discontinuous and its ability to handle complex topography easily.This paper is an assessment and comparison of the performance of ÿnite volume solutions to the shallow water equations with the Riemann solvers; the Osher, HLL, HLLC, ux di erence splitting (Roe) and ux vector splitting. In this paper implementation of the FVM including the Riemann solvers, slope limiters and methods used for achieving second order accuracy are described explicitly step by step. The performance of the numerical methods has been investigated by applying them to a number of examples from the literature, providing both comparison of the schemes with each other and with published results. The assessment of each method is based on ÿve criteria; ease of implementation, accuracy, applicability, numerical stability and simulation time. Finally, results, discussion, conclusions and recommendations for further work are presented.

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Group work can form a substantial component of degree programme assessments. To satisfy institutional and student expectations, students must often be assigned individual marks for their contributions to the group project, typically by mapping a single holistic group mark to individual marks using peer assessment scores. Since the early 1990s, various mapping methods that use self-and peer ratings have been developed. They are based on (normalised) individual weighting factors, partial scaling of the group mark, inter-rater agreement corrections or parabolic functions. We show that no single existing method can be successfully applied to most practical peer assessment scenarios such as different marking scale interpretations, intra-group ranking errors, biased free-riders and marks exceeding 100%. We present a combined analytical mapping method that incorporates the benefits of existing mechanisms, but alleviates their weaknesses with minimum computational effort and tutor input. The robustness of the method is illustrated through problematic assessment examples and empirically evaluated in multiple group work environments involving a total of 243 students and five different disciplines.