On the conservativity of the Particles-on-Demand method for the solution of the Discrete Boltzmann Equation It is well known that the standard Lattice-Boltzmann method (LBM) is applicable in the range of small flow velocities and under the isothermal conditions. The novel Particle-on-demand method [1] allows to numerically solve the discrete Boltzmann equation for high Mach numbers. We validate its capabilities with our implementation on the problems with shock waves. In comparison with the standard Lattice Boltzmann Method, the collision step is simple, but the streaming step is implicit, non-conservative and excessively computationally heavy. We propose a way that in specific cases improves the method by making the streaming step explicit and conservative. The results are validated by examining the total mass, momentum and energy change in the problem of shock formation due to the sound wave distortion. The scheme also performs well in both 1D and 3D test Sod problems.

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First-order phase transition at a fluctuation stage into non-linear dissipative plasma-like media is considered. The clustering of new phase germs (or nucleation) is represented by stochastic Wiener processes. Brownian motion of clusters induced by a long-range potential of indirect (through acoustic phonons and Friedel's oscillation of electron density) interaction between one another is taken into account. Kinetic models for blistering materials in a controlled thermonuclear reactor and for melted metal thin film islands deposition during surface CVD modification are both put forward. The non-steady-state distribution of clusters versus their size and position in space is calculated using Ito–Stratonovich stochastic differential equations. Formation of radiation stimulated porosity layers in a lattice as well as liquid island chains on the surface are to be discussed as characteristics of phase transition at fluctuation stages as well as a new kind of self-organization phenomenon.

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