We study two-dimensional turbulent compressible convection flow in a stable-unstable-stable configuration using numerical simulation. Our focus is on the mixing of passive tracer material from the unstable layer into the stable layer below. Two techniques, the Contour Advection with Surgery (CAS) method and the Particle Tracing Method (PTAM) are compared for their performances in describing the location and concentration of the tracer material. The main results are as following: (i) For this kind of problem (with turbulent flow), PTM is found to be better than the CAS method. The CAS method can describe the evolution of the tracer material boundary well in the beginning stage, but the quality soon deteriorates and the computer time shoots up quickly as the interface is made very complic...[ Read more ]

We study two-dimensional turbulent compressible convection flow in a stable-unstable-stable configuration using numerical simulation. Our focus is on the mixing of passive tracer material from the unstable layer into the stable layer below. Two techniques, the Contour Advection with Surgery (CAS) method and the Particle Tracing Method (PTAM) are compared for their performances in describing the location and concentration of the tracer material. The main results are as following: (i) For this kind of problem (with turbulent flow), PTM is found to be better than the CAS method. The CAS method can describe the evolution of the tracer material boundary well in the beginning stage, but the quality soon deteriorates and the computer time shoots up quickly as the interface is made very complicated by the turbulence. (ii) The algorithm and the physical interpretation of PTM are simpler and by nature preclude such problem from arising. It is therefore more efficient, and it turns out that its diffusive errors are low. It can describe the situation as good as the CAS (both results essentially agree) in the initial stage when CAS is still computationally affordable. Beyond this stage, PTM is found to be able to preserve the identities of the tracer filled and void regions very well, for a long period of time. (iii) Continuing the our study with PTM for the long term development of the mixing, we find that the asymptotic distribution of the tracer particle density tends to be proportional to the fluid density rather than being uniform, as might have been expected in the ordinary nonstratified situation.