{'fraction_non_alphanumeric': 0.032719836400818, 'fraction_numerical': 0.0006816632583503749, 'mean_word_length': 5.116666666666666, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
APPLICATION OF HIGHER ORDER BATHYMETRY REPRESENTATION IN FIXED GRID SHALLOW WATER SOLVERS

Fixed grid and flexible mesh solvers for the depth averaged Navier-Stokes equations (Shallow Water Equations) discretise a 2D domain into cells and faces. Many solution schemes consider the cells and faces to be flat-bottomed and either ‘wet’ or ‘dry’ depending on whether the water surface elevation exceeds the cell centre or face centre elevation. This first order representation causes errors in the results that depend on mesh size, and in the case of fixed grid solvers, mesh rotation angle, and in the case of flexible mesh solvers, mesh design. In this study we apply ‘Sub-Grid-Sampling’, a higher-order representation that considers ‘partially wet cells’ The mesh alignment and size sensitivities have been investigated by conducting numerical simulations of a U-shaped channel flume experiment, and a real-world meandering river with high quality of historical flood recordings. The benefits of ‘Sub-Grid-Sampling’ appear significant and far-reaching. At curved channels that are not mesh aligned, velocity fields no longer display “saw-tooth” patterns which cause artefact energy losses. Moreover, the sensitivities of results to mesh alignment and size are substantially reduced. This achievement is far-reaching in that fixed grid solvers with ‘Sub-Grid-Sampling’ can produce the same quality of results as a well-designed flexible mesh model or a cut-cell model.