What are some real-world examples of compressible fluid mechanics in action?

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SUMMARY

The discussion centers on the compressible Euler Equations, specifically the equations governing fluid dynamics in compressible flow. Participants seek non-trivial, multi-dimensional examples of functions that satisfy these equations, which include the conservation of mass and momentum. The equations are defined as follows: ∂t(ρu) + (u·∇)(ρu) + ∇p = 0 and ∂tρ + ∇·(ρu) = 0. The focus is on finding suitable initial conditions and solutions for the velocity vector u and density ρ.

PREREQUISITES
  • Understanding of compressible fluid dynamics
  • Familiarity with the compressible Euler Equations
  • Knowledge of vector calculus and partial differential equations
  • Experience with initial value problems in fluid mechanics
NEXT STEPS
  • Research multi-dimensional solutions to the compressible Euler Equations
  • Explore numerical methods for solving partial differential equations in fluid dynamics
  • Study real-world applications of compressible flow, such as supersonic jets
  • Investigate the role of initial conditions in determining fluid behavior
USEFUL FOR

Fluid dynamics researchers, mechanical engineers, and students studying compressible flow mechanics will benefit from this discussion.

dcs23
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Hi Guys,

I know that the compressible Euler Equations are:

\partial_t (\rho \mathbf u) + (\mathbf u \cdot \nabla)(\rho \mathbf u) + \nabla p = 0

\partial_t \rho + \nabla \cdot (\rho \mathbf u) = 0

Subject to suitable initial conditions and solving for \mathbf u, \; \rho unknown.

Does anybody have an example of a pair of functions which satisfies these relations in a non-1D case?
 
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Non trivial solutions would also be nice
 

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