Abstract
This paper presents a new finite volume scheme to efficiently simulate gravity currents flowing over complex surfaces. The two-dimensional shallow-water equations, with terms to account for friction and particle transport, are solved using a non-oscillatory technique. By applying a form drag at the front or head of the dense current, the scheme also implicitly captures the correct Froude number condition at the moving front as it intrudes into the less dense ambient fluid. The Froude number of the head region predicted by the numerical simulation is in good agreement with experimental results for a homogeneous current over a horizontal surface if a realistic profile drag coefficient is chosen. This new scheme avoids the development complexities of a general front-tracking scheme (e.g., handling merging fronts and multiple currents) and the computational cost of solving the full three-dimensional Euler equations while providing a fast, accurate simulation of gravity currents.
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