Riemann problems

A Riemann problem is a fundamental concept in mathematical physics and fluid dynamics involving the evolution of a system with a sudden change or discontinuity, like a shock wave or a boundary between different states. It starts with known, constant conditions on either side of a point, and the goal is to determine how these conditions evolve over time. Think of it as analyzing how a sudden jolt or switch in a system's initial state develops and propagates, helping scientists understand complex behaviors like shock waves, traffic flow, or weather patterns.