Rayleigh-Taylor-instability  induced flow and mixing are of great importance both in nature and engineering scenarios. To capture the underpinning physics, one-way coupled particles are introduced to make a Lagrangian tracking supplement to the discrete Boltzmann simulation . Detailed morphological information of the flow field and thermodynamic nonequilibrium behavior around the interfaces in a two-miscible-fluid system are delineated. Via a defined local mixedness , from densities of two kinds of particles, we quantitatively captured the appearance position and indicated the intensity of Kelvin-Helmholtz instability. The effects of compressibility and viscosity on mixing are investigated separately . Both of them show two-stage effects on mixing process . The underlying mechanism of these two-stage effects is interpreted as that a "hard" system with low compressibility and/or high viscosity is beneficial to the development of large structures at the initial stage and a "soft" system with high compressibility and/or low viscosity is favorable for the generation of small structures at the late stage. At the late stage, for a fixed time, the field averaged mixedness exponentially decreases with the viscosity , which indicates the existence of a characteristic viscosity \mu_0. The tracer particles make possible to observe finer structures with clear interfaces in the late mixing stage. One can clearly observe the mixing process and distinguish tracer particles from the heavy and light fluids . Results in this paper are helpful for understanding the mechanism of complex compressible flow with Rayleigh-Taylor instability and present references for related particle tracking experiments .
Rayleigh-Taylor-instability (RTI) induced flow and mixing are of great importance in both nature and engineering scenarios. To capture the underpinning physics, tracers are introduced to make a supplement to discrete Boltzmann simulation of RTI in compressible flows. Via marking two types of tracers with different colors, the tracer distribution provides a clear boundary of two fluids during the RTI evolution. Fine structures of the flow and thermodynamic nonequilibrium behavior around the interface in a miscible two-fluid system are delineated. Distribution of tracers in its velocity phase space makes a charming pattern showing quite dense information on the flow behavior, which opens a new perspective for analyzing and accessing significantly deep insights into the flow system. RTI mixing is further investigated via tracer defined local mixedness . The appearance of Kelvin-Helmholtz instability is quantitatively captured by mixedness averaged align the direction of the pressure gradient. The role of compressibility and viscosity on mixing are investigated separately , both of which show two-stage effect . The underlying mechanism of the two-stage effect is interpreted as the development of large structures at the initial stage and the generation of small structures at the late stage. At the late stage, for a fixed time, a saturation phenomenon of viscosity is found that further increase of viscosity cannot see an evident decline in mixedness. The mixing statues of heavy and light fluids are not synchronous and the mixing of a RTI system is heterogenous. The results are helpful for understanding the mechanism of flow and mixing induced by RTI .
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