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Lecture 1

Free-Surface Flow Simulation in Civil and Mechanical Engineering

Flow simulation plays an increasingly important role in all aspects of engineering, including civil and environmental engineering. Large-scale systems such as oceans, reservoirs and waterways need to be considered, along with smaller systems such as storage tanks or ships. For man-made systems, the computational analysis can result in more cost-effective and substantially faster development cycles, and for naturally-occuring systems, simulation offers an often shorter path to scientific understanding. We begin with a general introduction to discretization methods for problems governed by partial differential equations. We then focus on finite element methods for flow simulation, and the challenges including advection-dominated problems and the need for compatible velocity-pressure interpolations. Afterwards, the emphasis is placed on deforming domain problems, space-time discretizations, and mesh update techniques. Aspects of the simulations which are specific to free-surface flows are considered, including the kinematic boundary condition at the free surface and other boundary conditions.

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