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The sloshing phenomenon in a partially loaded oil tanker or liquid natural gas ship is a typical fluid-structure interaction problem involving multi-physics, violent free-surface flow, and nonlinear structural response. In the past decades, the complex phenomenon has been commonly investigated without consideration of the hydro-elastic behaviors of the bulkheads. In our previous work, the liquid sloshing phenomenon in a two-dimensional (2-D) elastic tank was numerically studied. However, the bulkheads of the tank will deform within the three-dimensional (3-D) space in reality. So, it is necessary to study the 3-D sloshing problem in an elastic tank. In this article, a hybrid approach is developed within the Lagrangian system. The moving particle semiimplicit (MPS) method is used to simulate the evolution of 3-D flow with a violent free surface, and the finite element method (FEM) is used for the numerical analysis of structural response due to the impact loads of the sloshing flow. To couple the MPS method and the FEM method, an interpolation scheme based on the kernel function of the particle method is proposed for the communication on the isomerous interface between the fluid and structure domains. The reliability of force and deformation interpolation modules is validated by two tests. Then, the sloshing phenomenon in a 3-D elastic tank is numerically investigated and compared against the previous published 2-D results. By varying the Young's modulus of the tank walls, characteristics regarding the evolutions of free surface, variation of impact pressures, and dynamic responses of the structures are presented. 1. Introduction To support the transportation demands of natural resources, more and more vessels, such as the very large crude carriers and the liquid natural gas carriers, are manufactured. For these huge structures, risks such as local deformation or even damage of cargo-containment systems resulting from sloshing phenomena subsequently increase. Therefore, it is necessary to take the elasticity of the tank walls into account in the research of sloshing phenomena (Dias & Ghidaglia 2018). However, the phenomena involving the vibrations of the tank walls are complex. In the process of sloshing wave interacting with elastic bulkheads, the fragmentation, splash, and fusion of water are observed. Meanwhile, the structures vibrate nonlinearly under the impact loads resulting from the sloshing wave. These phenomena are hard to simulate realistically by the traditional mesh-based methods.

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The mission of the low aspect ratio spherical tokamak NSTX-U is to advance the physics basis and technical solutions required for optimizing the configuration of next-step steady-state tokamak fusion devices. NSTX-U will ultimately operate at up to 2 MA of plasma current and 1 T toroidal field on axis for 5 seconds, and has available up to 15 MW of Neutral Beam Injection (NBI) power at different tangency radii and 6 MW of High Harmonic Fast Wave (HHFW) heating. With these capabilities NSTX-U will develop the physics understanding and control tools to ramp-up and sustain high performance fully non-inductive plasmas with large bootstrap fraction and enhanced confinement enabled via the low aspect ratio, high beta configuration. With its unique capabilities, NSTX-U research also supports ITER and other critical fusion development needs. Super-Alfvénic ions in beam-heated NSTX-U plasmas access energetic particle parameter space that is relevant for both -heated conventional and low aspect ratio burning plasmas. NSTX-U can also generate very large target heat fluxes to test conventional and innovative plasma exhaust and plasma facing component (PFC) solutions. This paper summarizes recent analysis, theory and modelling progress to advance the tokamak physics basis in the areas of macrostability and 3D fields, energetic particle stability and fast ion transport, thermal transport and pedestal structure, boundary and plasma material interaction, RF heating, scenario optimization and real-time control.