A Discontinuous Galerkin Morphodynamic Model with Orthogonal Bubble Function Boundary Treatment for River Flows
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Floods and channel adjustments in alluvial rivers arise from tightly coupled interactions among free-surface flow, sediment transport, and evolving bathymetry. Reliable morphodynamic prediction remains challenging, particularly near solid boundaries where complex bank geometry and imperfect wall-condition enforcement can generate spurious near-bank velocities, biased shear stresses, and unrealistic patterns of erosion and deposition. Building on our previously developed discontinuous Galerkin (DG) morphodynamic model, which employs an orthogonal bubble-function enrichment to improve solid-wall boundary treatment, we present a further enhancement aimed at geometric consistency along irregular banks. The framework combines linear triangular elements in the interior with orthogonal bubble-function elements along solid boundaries, enabling efficient and stable enforcement of the no-normal-flow condition. In this presentation, we introduce a nodal normal-vector technique that provides a smooth and continuous representation of boundary orientation, thereby improving the robustness and accuracy of near-bank flow and sediment-flux computations. The model is evaluated through a set of verification and validation studies, demonstrating accurate hydrodynamics and reliable prediction of bed evolution. We further examine the influence of secondary-flow parameterizations on bar dynamics and associated bed-change processes, highlighting their implications for morphodynamic sensitivity and uncertainty in practical river simulations. Overall, the proposed DG framework provides a stable and accurate tool for environmental fluid mechanics applications involving river morphodynamics and offers a flexible basis for extension to more complex hydro-morphodynamic processes.
