.. _sphx_glr__as_gen_gsph:

GSPH Examples
=============


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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="Advects a density jump at uniform velocity with equal pressure on both sides. Since p_L=p_R and u_L=u_R, the exact Riemann solution at the interface is a pure contact discontinuity: no shock or rarefaction forms, and the analytic solution is simply the initial density jump translated rigidly at speed u_0. This isolates how much a scheme numerically diffuses a density (compositional) interface carried by a uniform flow, independent of any shock-capturing behaviour.">

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  .. image:: /_as_gen/gsph/images/thumb/sphx_glr_run_advection_thumb.png
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  :doc:`/_as_gen/gsph/run_advection`

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      <div class="sphx-glr-thumbnail-title">Contact-discontinuity advection with GSPH (exact Riemann solver + Inutsuka V2)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Runs a 3D Sod shock tube using the Godunov SPH (GSPH) solver with the exact Riemann solver (Toro 2009) and the Inutsuka (2002) effective volume/face force formulation, and compares the result against the analytic solution.">

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  .. image:: /_as_gen/gsph/images/thumb/sphx_glr_run_sod_thumb.png
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  :doc:`/_as_gen/gsph/run_sod`

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      <div class="sphx-glr-thumbnail-title">Sod shock tube with GSPH (exact Riemann solver + Inutsuka V2)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Severe shock-tube problem from Inutsuka (2002, Section 4.3), with a pressure ratio of 3\times10^{10} and a peak Mach number around 10^5. Both sides start at rest with equal density (\rho_L=\rho_R=1, P_L=3000, P_R=10^{-7}), so this is a Sod-type (zero-velocity) discontinuity for which the analytic solution is available via shamrock.phys.SodTube. It stress-tests the solver&#x27;s stability at extreme pressure/Mach ratios rather than its wave-pattern classification.">

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  .. image:: /_as_gen/gsph/images/thumb/sphx_glr_run_blast_wave_thumb.png
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  :doc:`/_as_gen/gsph/run_blast_wave`

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      <div class="sphx-glr-thumbnail-title">Extreme blast wave with GSPH (exact Riemann solver + Inutsuka V2)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Two identical bodies of gas move apart from a common interface at high speed (\rho_L=\rho_R=1, u_L=-2, u_R=+2, p_L=p_R=0.4). This is Toro&#x27;s standard &quot;Test 2&quot; benchmark: both waves are rarefactions, and they drive the star-region pressure to near vacuum (p^*/p_L\approx 4.7\times10^{-3}). It is the classical stress test for solver robustness near vacuum conditions, where linearized/approximate Riemann solvers are prone to returning negative pressure or density.">

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  .. image:: /_as_gen/gsph/images/thumb/sphx_glr_run_123_problem_thumb.png
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  :doc:`/_as_gen/gsph/run_123_problem`

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      <div class="sphx-glr-thumbnail-title">Toro's "123 problem" with GSPH (exact Riemann solver + Inutsuka V2)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Two identical bodies of gas move toward each other at equal and opposite speed (\rho_L=\rho_R=1, u_L=+1, u_R=-1, p_L=p_R=1). By symmetry the contact stays fixed at u^*=0 for all time, which makes this equivalent to each half of the gas hitting a rigid, reflecting wall at x=0. This is the standard &quot;wall collision&quot; test used to check that a scheme does not produce spurious post-shock heating at a symmetry plane -- a known pathology of artificial-viscosity SPH that Riemann-solver formulations such as GSPH are designed to avoid.">

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  .. image:: /_as_gen/gsph/images/thumb/sphx_glr_run_symmetric_collision_thumb.png
    :alt:

  :doc:`/_as_gen/gsph/run_symmetric_collision`

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      <div class="sphx-glr-thumbnail-title">Symmetric gas collision with GSPH (exact Riemann solver + Inutsuka V2)</div>
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    </div>


.. toctree::
   :hidden:

   /_as_gen/gsph/run_advection
   /_as_gen/gsph/run_sod
   /_as_gen/gsph/run_blast_wave
   /_as_gen/gsph/run_123_problem
   /_as_gen/gsph/run_symmetric_collision