The state-of-the-art engineering and ocean science models are based on the Navier–Stokes (NS) equations and the geophysical fluid dynamics (GFD) equations, respectively. This chapter presents a multiblock modeling system that couples the NS equations and the GFD equations in two ways to simulate emerging multiscale, multiphysics ocean flows, especially local, complex phenomena. In the NS-GFD model system, the NS equations are solved by a finite difference method, and the GFD equations are solved by a finite volume method. The model system extends the framework and the overset-grid techniques, including the grid-connectivity and interface algorithms, of the previous chapters, and it also adopts a pressure split technique to couple the NS and GFD equations. Numerical examples, including a sill flow, a current past bridge piers, and a thermal-effluent discharge into a realistic ocean, illustrate the promise of the NS-GFD model system. However, difficulties such as non-physical phenomena may occur in numerical solutions, e.g., at NS-GFD interfaces. Then, this chapter discusses methods to overcome these difficulties, explores interface conditions, and includes example simulations to demonstrate their performance. Additionally, it extends the framework of the NS-GFD model system to couple the shallow water equations with the GFD equations and presents numerical experiments on a surface tide, a dam-break flow, and a coastal flood.

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Coastal Ocean Flow

  • Hansong Tang

摘要

The state-of-the-art engineering and ocean science models are based on the Navier–Stokes (NS) equations and the geophysical fluid dynamics (GFD) equations, respectively. This chapter presents a multiblock modeling system that couples the NS equations and the GFD equations in two ways to simulate emerging multiscale, multiphysics ocean flows, especially local, complex phenomena. In the NS-GFD model system, the NS equations are solved by a finite difference method, and the GFD equations are solved by a finite volume method. The model system extends the framework and the overset-grid techniques, including the grid-connectivity and interface algorithms, of the previous chapters, and it also adopts a pressure split technique to couple the NS and GFD equations. Numerical examples, including a sill flow, a current past bridge piers, and a thermal-effluent discharge into a realistic ocean, illustrate the promise of the NS-GFD model system. However, difficulties such as non-physical phenomena may occur in numerical solutions, e.g., at NS-GFD interfaces. Then, this chapter discusses methods to overcome these difficulties, explores interface conditions, and includes example simulations to demonstrate their performance. Additionally, it extends the framework of the NS-GFD model system to couple the shallow water equations with the GFD equations and presents numerical experiments on a surface tide, a dam-break flow, and a coastal flood.