Magnetized target fusion is a relatively new idea for producing conditions for hydrogen fusion on earth. The essence of the idea is to confine a plasma in a magnetic field and compress it by an intense pressure-focused pulse so that it yields a high enough particle density and pressure for fusion to take place, releasing energy. A Canadian research company has a design of such an apparatus that they are currently working on engineering: the plasma is found in an empty region of a vertical central cylindrical axis of a sphere of molten lead-lithium. Pistons deliver an immense pressure on the outer walls of the spherical lead-lithium region, with the pressure growing in magnitude as it reaches the plasma, causing it to compress to a very small radius. Simulating this design requires a careful interplay of plasma physics and fluid dynamics, and reasonable modelling skills. My research interest here is in developing a suitable model, performing numerical simulations for the hyperbolic conservation laws, and doing asymptotic analysis to estimate the influence of various factors on the reactor performance qualitatively and analytically, and studying how asymmetries in the implosion affect the quality of compression.