Abstract. Morphological measures are introduced to probe the complex procedure of shock wave reaction on porous material. They characterize the geometry and topology of the pixelized map of a state variable like the temperature. Relevance of them to thermodynamical properties of material is revealed and various experimental conditions are simulated. Numerical results indicate that, the shock wave reaction results in a complicated sequence of compressions and rarefactions in porous material. The increasing rate of the total fractional white area A roughly gives the velocity D of a compressive-wave-series. When a velocity D is mentioned, the corresponding threshold contour-level of the state variable, like the temperature, should also be stated. When the threshold contour-level increases, D becomes smaller. The area A increases parabolically with time t during the initial period. The A(t) curve goes back to be linear in the following three cases: (i) when the porosity δ approaches 1, (ii) when the initial shock becomes stronger, (iii) when the contour-level approaches the minimum value of the state variable. The area with high-temperature may continue to increase even after the early compressive-waves have arrived at the downstream free surface and some rarefactive-waves have come back into the target body. In the case of energetic material needing a higher temperature for initiation, a higher porosity is preferred and the material may be initiated after the precursory compressive-waves have scanned all the target body. One may desire the fabrication of a porous body and choose appropriate shock strength according to what needed is scattered or connected hotspots. With the Minkowski measures, the dependence on experimental conditions is reflected simply by a few coefficients. They may be used as order parameters to classify the maps of physical variables in a similar way like thermodynamic phase transitions.Submitted to: J. Phys. D: Appl. Phys.

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We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara [Phys. Rev. E 69, 056702 (2004)] and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number up to 30 (or higher), which is validated by well-known benchmark tests. Simulations on Riemann problems with very high ratios (1000 : 1) of pressure and density also show good accuracy and stability. Successful recovering of regular and double Mach shock reflections shows the potential application of the lattice Boltzmann model to fluid systems where non-equilibrium processes are intrinsic. The new scheme for stability can be easily extended to other lattice Boltzmann models.

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