Interface Tracking and Solid-Fluid Coupling Techniques with Coastal Engineering Applications

摘要

Multi-material physics arise in an innumerable amount of engineering problems. A broadlyudscoped numerical model is developed and described in this thesis to simulate the dynamic interactionudof multi-fluid and solid systems. It is particularly aimed at modelling the interactionudof two immiscible fluids with solid structures in a coastal engineering context; however it canudbe extended to other similar areas of research. The Navier Stokes equations governing theudfluids are solved using a combination of finite element (FEM) and control volume finite elementud(CVFE) discretisations. The sharp interface between the fluids is obtained through theudcompressive transport of material properties (e.g. material concentration). This behaviour isudachieved through the CVFE method and a conveniently limited flux calculation scheme basedudon the Hyper-C method by Leonard (1991). Analytical and validation test cases are provided,udconsisting of steady and unsteady flows. To further enhance the method, improve accuracy, andudexploit Lagrangian benefits, a novel moving mesh method is also introduced and tested. It isudessentially an Arbitrary Lagrangian Eulerian method in which the grid velocity is defined byudsemi-explicitly solving an iterative functional minimisation problem.udA multi-phase approach is used to introduce solid structure modelling. In this approach,udsolution of the velocity field for the fluid phase is obtained using Model B as explained byudGidaspow (1994, page 151). Interaction between the fluid phase and the solids is achievedudthrough the means of a source term included in the fluid momentum equations. The interactingudforce is calculated through integration of this source term and adding a buoyancy contribution.udThe resulting force is passed to an external solid-dynamics model such as the Discrete ElementudMethod (DEM), or the combined Finite Discrete Element Method (FEMDEM).udThe versatility and novelty of this combined modelling approach stems from its ability toudcapture the fluid interaction with particles of random size and shape. Each of the three mainudcomponents of this thesis: the advection scheme, the moving mesh method, and the solid interactionudare individually validated, and examples of randomly shaped and sized particles areudshown. To conclude the work, the methods are combined together in the context of coastal engineeringudapplications, where the complex coupled problem of waves impacting on breakwaterudamour units is chosen to demonstrate the simulation possibilities. The three components developedudin this thesis significantly extend the application range of already powerful tools, suchudas Fluidity, for fluids-modelling and finite discrete element solids-modelling tools by bringingudthem together for the first time.