.. _sphx_glr_api_gallery_fluids_compressible_flow:

Compressible Flow
-----------------

Once a flow moves fast enough that the fluid can no longer get out of its
own way, incompressible potential and viscous flow stop applying entirely:
the 1D Euler equations support genuinely discontinuous solutions that no
smooth velocity field can produce. The normal-shock example sweeps the
upstream Mach number through the exact Rankine-Hugoniot jump relations,
showing a supersonic flow is always driven back to subsonic on the other
side of a shock, at the cost of a sharp pressure and density jump. The Sod
shock tube then resolves that same jump dynamically, from a simple burst
initial condition, alongside the two other waves -- a rarefaction fan and a
contact discontinuity -- that a general compressible flow problem produces
alongside a shock. Watch, in the shock-tube profiles, how a first-order
finite-volume scheme smears the shock over several cells even as it gets
its speed and downstream state right.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="A normal shock is a stationary discontinuity, perpendicular to the flow, in an otherwise steady 1D inviscid compressible flow of an ideal gas: state 1 (upstream) and state 2 (downstream) must conserve mass, momentum, and energy flux across it exactly (the Rankine-Hugoniot conditions, rankine_hugoniot_jump_conditions). Solved for an ideal gas, these give the downstream state entirely as a function of the upstream Mach number M_1=u_1/c_1:">

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  .. image:: /api/gallery/fluids/compressible_flow/images/thumb/sphx_glr_plot_normal_shock_thumb.png
    :alt:

  :doc:`/api/gallery/fluids/compressible_flow/plot_normal_shock`

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      <div class="sphx-glr-thumbnail-title">Normal shock relations across a range of Mach numbers</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Sod&#x27;s (1978) shock-tube problem is the standard test Riemann problem for a compressible-flow solver: a diaphragm at x_0 initially separates high-pressure, high-density gas at rest from low-pressure, low-density gas at rest,">

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  .. image:: /api/gallery/fluids/compressible_flow/images/thumb/sphx_glr_plot_sod_shock_tube_thumb.png
    :alt:

  :doc:`/api/gallery/fluids/compressible_flow/plot_sod_shock_tube`

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      <div class="sphx-glr-thumbnail-title">The Sod shock tube</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/fluids/compressible_flow/plot_normal_shock
   /api/gallery/fluids/compressible_flow/plot_sod_shock_tube