Stefan Stefanov

Bio: Stefan Stefanov is an academic researcher from Bulgarian Academy of Sciences. The author has contributed to research in topics: Direct simulation Monte Carlo & Knudsen number. The author has an hindex of 22, co-authored 115 publications receiving 1320 citations. Previous affiliations of Stefan Stefanov include National Academy of Sciences of Belarus & Ferdowsi University of Mashhad.

On DSMC Calculations of Rarefied Gas Flows with Small Number of Particles in Cells

Abstract: The direct simulation Monte Carlo (DSMC) analysis of two- and three-dimensional rarefied gas flows requires computational resources of very large proportions. One of the major causes for this is that, along with the multidimensional computational mesh, the standard DSMC approach also requires a large number of particles in each cell of the mesh in order to obtain sufficiently accurate results. This paper presents the development and validation of a modified simulation procedure which allows more accurate calculations with a smaller mean number of particles ($\langle N\rangle\sim1$) in the grid cells. In the new algorithm, the standard DSMC collision scheme is replaced by a two-step collision procedure based on “Bernoulli trials” scheme (or its simplified version proposed by the author), which is applied twice to the cells (or subcells) of a dual grid within a time step. The modified algorithm uses a symmetric Strang splitting scheme that improves the accuracy of the splitting scheme to $O(\tau^2)$ with respect to the time step $\tau$, making the modified DSMC method an effective numerical tool for both steady and unsteady gas flow calculations on fine multidimensional grids. The latter is particularly important for simulation of vortical and unstable rarefied gas flows. The modified simulation scheme might also be useful for DSMC calculations within the subcell areas of a multilevel computational grid.

Rayleigh-Bénard flow of a rarefied gas and its attractors. I. Convection regime

Abstract: In this paper we investigate the long time behavior (final state) of the Rayleigh–Benard (RB) flow of a rarefied monatomic gas for a set of the nondimensional Knudsen and Froude numbers in the intervals Kn∈[1.0×10−3,4×10−2], Fr∈[1.0×10−1,1.5×103]. For the most part of the computations the third nondimensional parameter, the ratio of the cold and hot wall temperatures is fixed to Tc/Th=0.1, corresponding to a large temperature difference (Th serves as reference temperature), for which the RB system is believed to reach most of the possible final states (attractors). The low Knudsen numbers allow the problem to be investigated numerically by using two completely different methods: direct simulation Monte Carlo (DSMC) method (molecular approach) and finite difference (FD) method (continuum approach based on the model of compressible viscous heat conducting gas with state-dependent transport coefficients). As a result the effect of rarefaction on the onset of convection in the two-dimensional case is studied ...

Thermal and second-law analysis of a micro- or nanocavity using direct-simulation Monte Carlo

Abstract: In this study the direct-simulation Monte Carlo (DSMC) method is utilized to investigate thermal characteristics of micro- or nanocavity flow. The rarefied cavity flow shows unconventional behaviors which cannot be predicted by the Fourier law, the constitutive relation for the continuum heat transfer. Our analysis in this study confirms some recent observations and shows that the gaseous flow near the top-left corner of the cavity is in a strong nonequilibrium state even within the early slip regime, Kn=0.005. As we obtained slip velocity and temperature jump on the driven lid of the cavity, we reported meaningful discrepancies between the direct and macroscopic sampling of rarefied flow properties in the DSMC method due to existence of nonequilibrium effects in the corners of cavity. The existence of unconventional nonequilibrium heat transfer mechanisms in the middle of slip regime, Kn=0.05, results in the appearance of cold-to-hot heat transfer in the microcavity. In the current study we demonstrate that existence of such unconventional heat transfer is strongly dependent on the Reynolds number and it vanishes in the large values of the lid velocity. As we compared DSMC solution with the results of regularized 13 moments (R13) equations, we showed that the thermal characteristic of the microcavity obtained by the R13 method coincides with the DSMC prediction. Our investigation also includes the analysis of molecular entropy in the microcavity to explain the heat transfer mechanism with the aid of the second law of thermodynamics. To this aim, we obtained the two-dimensional velocity distribution functions to report the molecular-based entropy distribution, and show that the cold-to-hot heat transfer in the cavity is well in accordance with the second law of thermodynamics and takes place in the direction of increasing entropy. At the end we introduce the entropy density for the rarefied flow and show that it can accurately illustrate departure from the equilibrium state.

Monte Carlo simulation of the Taylor–Couette flow of a rarefied gas

Abstract: We report and discuss the results of a direct Monte Carlo simulation of the flow of a rarefied gas flowing between two cylinders when the inner one rotates. The formation of Taylor vortices is clearly exhibited.

Fast parallel algorithms for short-range molecular dynamics

Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Kinetic Theory and Fluid Dynamics

Abstract: In this series of talks, I will discuss the fluid-dynamic-type equations that is derived from the Boltzmann equation as its the asymptotic behavior for small mean free path. The study of the relation of the two systems describing the behavior of a gas, the fluid-dynamic system and the Boltzmann system, has a long history and many works have been done. The Hilbert expansion and the Chapman–Enskog expansion are well-known among them. The behavior of a gas in the continuum limit, however, is not so simple as is widely discussed by superficial understanding of these solutions. The correct behavior has to be investigated by classifying the physical situations. The results are largely different depending on the situations. There is an important class of problems for which neither the Euler equations nor the Navier–Stokes give the correct answer. In these two expansions themselves, an initialor boundaryvalue problem is not taken into account. We will discuss the fluid-dynamic-type equations together with the boundary conditions that describe the behavior of the gas in the continuum limit by appropriately classifying the physical situations and taking the boundary condition into account. Here the result for the time-independent case is summarized. The time-dependent case will also be mentioned in the talk. The velocity distribution function approaches a Maxwellian fe, whose parameters depend on the position in the gas, in the continuum limit. The fluid-dynamictype equations that determine the macroscopic variables in the limit differ considerably depending on the character of the Maxwellian. The systems are classified by the size of |fe− fe0|/fe0, where fe0 is the stationary Maxwellian with the representative density and temperature in the gas. (1) |fe − fe0|/fe0 = O(Kn) (Kn : Knudsen number, i.e., Kn = `/L; ` : the reference mean free path. L : the reference length of the system) : S system (the incompressible Navier–Stokes set with the energy equation modified). (1a) |fe − fe0|/fe0 = o(Kn) : Linear system (the Stokes set). (2) |fe − fe0|/fe0 = O(1) with | ∫ ξifedξ|/ ∫ |ξi|fedξ = O(Kn) (ξi : the molecular velocity) : SB system [the temperature T and density ρ in the continuum limit are determined together with the flow velocity vi of the first order of Kn amplified by 1/Kn (the ghost effect), and the thermal stress of the order of (Kn) must be retained in the equations (non-Navier–Stokes effect). The thermal creep[1] in the boundary condition must be taken into account. (3) |fe − fe0|/fe0 = O(1) with | ∫ ξifedξ|/ ∫ |ξi|fedξ = O(1) : E+VB system (the Euler and viscous boundary-layer sets). E system (Euler set) in the case where the boundary is an interface of the gas and its condensed phase. The fluid-dynamic systems are classified in terms of the macroscopic parameters that appear in the boundary condition. Let Tw and δTw be, respectively, the characteristic values of the temperature and its variation of the boundary. Then, the fluid-dynamic systems mentioned above are classified with the nondimensional temperature variation δTw/Tw and Reynolds number Re as shown in Fig. 1. In the region SB, the classical gas dynamics is inapplicable, that is, neither the Euler

Microbial steroid transformations: current state and prospects

Abstract: Studies of steroid modifications catalyzed by microbial whole cells represent a well-established research area in white biotechnology. Still, advances over the last decade in genetic and metabolic engineering, whole-cell biocatalysis in non-conventional media, and process monitoring raised research in this field to a new level. This review summarizes the data on microbial steroid conversion obtained since 2003. The key reactions of structural steroid functionalization by microorganisms are highlighted including sterol side-chain degradation, hydroxylation at various positions of the steroid core, and redox reactions. We also describe methods for enhancement of bioprocess productivity, selectivity of target reactions, and application of microbial transformations for production of valuable pharmaceutical ingredients and precursors. Challenges and prospects of whole-cell biocatalysis applications in steroid industry are discussed.

Rarefaction and compressibility effects on steady and transient gas flows in microchannels

Abstract: The main theoretical and experimental results from the literature about steady pressure-driven gas microflows are summarized. Among the different gas flow regimes in microchannels, the slip flow regime is the most frequently encountered. For this reason, the slip flow regime is particularly detailed and the question of appropriate choice of boundary conditions is discussed. It is shown that using second-order boundary conditions allows us to extend the applicability of the slip flow regime to higher Knudsen numbers that are usually relevant to the transition regime. The review of pulsed flows is also presented, as this kind of flow is frequently encountered in micropumps. The influence of slip on the frequency behavior (pressure gain and phase) of microchannels is illustrated. When subjected to sinusoidal pressure fluctuations, microdiffusers reveal a diode effect which depends on the frequency. This diode effect may be reversed when the depth is shrunk from a few hundred to a few μm. Thermally driven flows in microchannels are also described. They are particularly interesting for vacuum generation using microsystems without moving parts.