A Cartesian Cut-Cell Methodology, Applied to Large Scale Interface Dynamics and Wave Impacts Spray Formation
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The present thesis focus on developing numerical methods that can resolve various problems in computational fluid dynamics. The Cartesian cut-cell method is used to solve continuity and momentum equations. The method will help to tackle the difficulty of meshing complex object shapes. The Crank-Nicolson scheme is applied to compute the diffusive flux while th Adams-Bashforth scheme is employed to evaluate the convective flux. Therefore, the numerical result will be close to the second-order accuracy. A method for computing the convective and diffusive fluxes for cells near a wall is presented. Two different approaches are proposed to solve the instability problem from small cells, namely cell-linking and the flux distribution method. For two fluids flow, the embedded boundary method is employed to test the ability to apply cut-cell. Unfortunately, it did not succeed. Therefore, the ghost-fluid method is used instead. It is robust and easy to extend into 3D applications. The density-based computation of the convective flux is employed to avoid unphysical phenomena at the interface, which happens due to the large ratio between fluids densities. For tracking interface movement, the coupled level set and volume of fluid is used. The combination of the two approaches will improve the overall accuracy of computing interface configurations. The finite volume method is used to solve the transport equation for the liquid volume fraction and the level set function such that mass conservation will be improved. In order to increase the accuracy of computing the normal vector for the free surface, a special technique, which is based on interface configuration, is proposed. For the development of the droplet generation model, the primary breakup, which is based on the surface wave instability, causes the liquid sheet to disintegrate into droplets. The idea is initiated from what we observe in an experiment when a thin liquid layer is formed after a wave impact to the wall. Then, droplets are produced from the liquid sheet. After that, a secondary breakup model is implemented to make the droplets transform into smaller ones. All liquid particle motion is described by the Lagrangian tracking method. The weak two-way coupling is used to represent the interaction between discrete droplets and continuous fluids. All source terms are treated implicitly to avoid instability problems.