The Developments and the Applications of the Numerical Algorithms in Simulating the Incompressible Magnetohydrodynamics with Complex Boundaries and Free Surfaces

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The thesis introduces an advanced numerical methodology to address challenges in simulating magnetohydrodynamic (MHD) flows, grid generation for tokamak fusion, and the interaction of surface tension and Lorentz forces in metallurgy. It explores topics like the motion of single bubbles in magnetic fields, revealing the connection between bubble path instability and wake instability. Additionally, it examines how vertical and horizontal magnetic fields affect vortex structures, influencing the dynamics of rising bubbles.