The Riemann Problem refers to a type of initial value problem in hyperbolic partial differential equations, which specifically focuses on solving equations that model waves and shocks in various physical contexts. This problem is essential for understanding how discontinuities, such as shock waves and contact discontinuities, evolve over time in fluid dynamics, particularly in magnetohydrodynamics. The solutions to the Riemann Problem can reveal intermediate shocks and rotational discontinuities, which are crucial for analyzing complex flow patterns.
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