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Scramjet Project

    Jet with crossflow

Uncertainty Quantification

        Errors in Numerical Solutions of Shock Physics Problems

            PowerPoint presentation from dissertation defense

 

        (with the constant pressure boundary condition driving a Mach

         2 Shock into the radial domain)

 

Animation

Mesh Size

Offset

Perturbation

Tin_400.gif

200X400

no

single mode

Tin_400_offset.gif

200X400

yes

single mode

Tin_800.gif

400X800

no

single mode

Tin_800_offset.gif

400X800

yes

single mode

Tin_1600.gif

800X1600

no

single mode

Tin_1600_offset.gif

800X1600

yes

single mode

100_rd.gif

100X200

no

random

100_rd_off.gif

100X200

yes

random

200_rd.gif

200X400

no

random

200_rd_off.gif

200X400

yes

random

400_rd.gif

400X800

no

random

400_rd_off.gif

400X800

yes

random

800_rd.gif

800X1600

no

random

800_rd_off.gif

800X1600

yes

random

 

   Above are LOG-DENSITY animations for implosion simulations in a two-dimensional geometry with two materials: Tin (heavy, outside of contact) and Lucite (light, inside of contact). The inner circle is the material boundary while the outer circle is set as a constant-pressure boundary.

    A Mach 2 shock was used in these simulations.  

    The stopping time for those runs was set to t = 80, at which time the driven shock has crossed the contact interface, hit the origin and produced a reflected shock which crosses the interface and eventually reaches the outer boundary.  

    The chaotic mixing of Tin and Lucite (respectively, the heavy and light materials) was produced by the driven and reflective shocks.

 

Below are the L-1 norms of the differences (errors) between successive grid levels.