## Fast transient fluid dynamics

EPX implements advanced fluid models and Finite Volume schemes for multi-component flow, reactive flows or multi-phasic flows. Below are some results for illustrative tests for which a reference solution is available :

- shock-bubble interaction simulations,
- water-gas Richtmeyer-Meshkov instabilities,
- Woodward-Colella wind tunnel with a step,
- validation of Hydrogen detonation model against experiments (FZK 12 meters shock tube).

**Shock-bubble interaction simulations**

Interaction of shock waves with cylindrical gas inhomogeneity is one of the standard shock bubble interaction problems, and it is treated as an example of the shock induced RMI *(Richtmyer-Meshkov Instability).*

A medium of air is hosting a cylindrical bubble filled with a gas which is either lighter (Helium) or heavier (R22) than air. In the initial state, a shock wave is travelling through the air, towards the cylindrical bubble. The deformation of the cylindrical, two-fluid interface and the resulting wave patterns strongly depend on the bubble gas properties:

*R22 bubble (experiment on the left, density field computer with EPX on the right)*

*Helium bubble (experiment on the left, density field computer with EPX on the right)*

*References:*

[1] J. F. Haas and B. Sturtevant, ¨Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities¨, Fluid Mech, Vo1 181, 41, (1987).

[2] J. J. Kreeft and B. Koren, ¨A new formulation of Kapila’s five-equation model for compressible two-fluid flow, and its numerical treatment¨, Computational Physics, Vol 229, 6220 , (2010).

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**Water-gas Richtmyer-Meshkov Instability**

The left part of the computational domain is filled with pure water while the right part with pure gas. They are initially separated by a curved interface. It is a portion of circle with 0.6 meter radius centered at x = 1.2 m, y = 0.5 m. The physical domain is 3 m long and 1 m high. Both water and gas have an initial velocity of – 200 m/s. Top, bottom and left boundaries are treated as solid walls.

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**Woodward-Colella wind tunnel with a Step**

The problem uses a two-dimensional rectangular domain three units wide and one unit high. Between *x*=0.6 and *x*=3 along the *x*-axis is a step 0.2 units high.

The step is treated as a reflecting boundary, as are the lower and upper boundaries in the *y* direction. For the right-hand *x* boundary we use an outflow (zero gradient) boundary condition, while on the left-hand side we use an inflow boundary. In the inflow boundary zones we set the density to 1.4, the pressure to 1, and the velocity to 3, with the latter directed parallel to the *x*-axis. With a gamma of 1.4, this corresponds to a Mach 3 flow.

*Reference*:

Colella, P.; Woodward, P. R. (1984). "The numerical simulation of two-dimensional fluid flow with strong shocks". J. Comput. Phys. (Elsevier) 54: 115–173.

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**Validation of Hydrogen detonation model against experiments (FZK 12 meters shock tube)**

*Impact of a detonation wave on an inclined plane target*