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The study of fluids has been a topic of intense research for several hundredyears. Over the years, this has further increased due to improved computationalfacility, which makes it easy to numerically simulate the fluid dynamics, whichwas beyond the analytical reach before. In this project, we discuss the generaltransport theorem for moving control volume system, apply this theory tocontrol mass system which gives the continuity equation, and on momentumconservation from which we get the Navier-Stokes equation and energyconservation. By approximating the three equations for the ideal gas flow, weget one dimensional Euler equation. These equations are non-linear, and theiranalytic solutions are highly non-trivial. We will use Riemann solvers to getthe exact solution numerically. In this project, we have considered only theSod's Shock Tube problem. Finally, we focus on the exact and approximatesolution of density, pressure, velocity, entropy, and Mach number using Pythoncode.

An Introduction to Fluid Dynamics and Numerical Solution of Shock Tube Problem by Using Roe Solver