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 magnetohydrodynamic (MHD) flow simulations within computational fluid dynamics (CFD), particularly in tokamak fusion and metallurgy. It explores topics like single bubble motion influenced by magnetic fields, revealing the connection between bubble path instability and wake instability. The research also examines how vertical and horizontal magnetic fields affect vortex structures, shedding light on their impact on the dynamics of rising bubbles.