Kiril S. Shterev

Pressure based finite volume method for calculation of compressible viscous gas flows

A pressure based, iterative finite volume method is developed for calculation of compressible, viscous, heat conductive gas flows at all speeds. The method does not need the use of under-relaxation coefficient in order to ensure a convergence of the iterative process. The method is derived from a general form of system of equations describing the motion of compressible, viscous gas. An emphasis is done on the calculation of gaseous microfluidic problems. A fast transient process of gas wave propagation in a two-dimensional microchannel is used as a benchmark problem. The results obtained by using the new method are compared with the numerical solution obtained by using SIMPLE (iterative) and PISO (non-iterative) methods. It is shown that the new iterative method is faster than SIMPLE. For the considered problem the new method is slightly faster than PISO as well. Calculated are also some typical microfluidic subsonic and supersonic flows, and the Rayleigh-Benard convection of a rarefied gas in continuum limit. The numerical results are compared with other analytical and numerical solutions.

Comparison of some approximation schemes for convective terms for solving gas flow past a square in a microchannel

Rapidly emerging micro-electro-mechanical devices create new potential microfluidic applications. A simulation of an internal and external gas flows is important for their design. For small Knudsen number Kn < 0.1 (Kn = l0/L, where l0 is the mean free path of the gas molecules and L is the characteristic length), a continuum approach based on modified Navier-Stokes-Fourier or extended hydrodynamic continuum models with corresponding velocity-slip and temperature-jump boundary conditions is still applicable and, respectively, preferable. We restrict ourself to the use of Navier-Stokes-Fourier continuum model. A development of the algorithm to solve a specific class of problems is closely related to numerical schemes used for approximation of equations terms. Higher-order approximation schemes can reduce the number of mesh nodes and respectively computational time, but it is possible to obtain physical unrealistic results. In this paper we study influence of some approximation schemes for convective terms o...

A parallel algorithm with improved performance of finite volume method (SIMPLE-TS)

In this paper a parallel version of the finite volume method SIMPLE-TS for calculation of two-dimensional compressible, viscous gas flows with improved performance is presented. It is demonstrated on a problem regarded to micro gas flows, taking place in Micro-Electro-Mechanical Systems (MEMS). The reorganisation of the parallel algorithm improve the algorithm performance, when more cores are used for calculations on computational grids with relatively small number of nodes or cells. The reorganisation is two-fold: first to reduce the number of communications between the processes, and second to reorder the calculation of some variables in such a way that increases the number of calculations during the communications between the processes. The comparison of speed-up between previous and new parallel versions of SIMPLE-TS was performed on two types of clusters with regard to the communication hardware: the first uses specialised cards with low latency for the interconnections between the computers and the other uses conventional cards for the interconnections. The clusters are a part of the GRID-infrastructure of the European Research Area (ERA).

GPU Calculations of Unsteady Viscous Compressible and Heat Conductive Gas Flow at Supersonic Speed

The recent trend of using Graphics Processing Units (GPUs) for high performance computations is driven by the high ratio of price performance for these units, complemented by their cost effectiveness. Such kinds of units are increasingly being deployed not only as accelerators for supercomputer installations, but also in GPU-enabled nodes in Grid and Cloud installations. At first glance computational fluid dynamics (CFD) solvers match perfectly to GPU resources, because these solvers make intensive calculations and use relatively small memory. Nevertheless, there are scarce results about the practical use of this serious advantage of GPU over CPU, especially for calculations of viscous, compressible, heat conductive gas flows with double precision accuracy. In our work we present calculation of unsteady, viscous, compressible and heat conductive gas with double precision accuracy using GPU-enabled version of the algorithm SIMPLE-TS, written on standard OpenCL. As a test case we model the flow past a square in a microchannel at supersonic speed with Mach number \(\mathrm{{M}}=2.43\) on AMD Radeon HD 7950 GPU and achieve 90 GFlops, which is 46 times faster than the CPU serial code run on Intel Xeon X5560.

A parallelization of finite volume method for calculation of gas microflows by domain decomposition methods

In this paper a parallel organization of a finite volume algorithm for calculation of two-dimensional compressible, viscous gas flows is presented The problem is addressed to the new emerging area of the micro gas flows, taking place in Micro-Electro-Mechanical Systems (MEMS) Technically, the parallel algorithm is organized by using standard MPI, non-blocking communications and the latency of the communications is overlapped with useful work The speedup was estimated on two clusters The first cluster uses MYRINET interconnections (BG04-ACAD) The second uses conventional cards for interconnections (BG03-NGCC) Both clusters are a part of GRID-infrastructure of the European Research Area (ERA) An ideal speedup is obtained on BG04-ACAD for a number of processors up to 20 CPUs The speedup obtained on BG03-NGCC is very good, however it depends on the mesh refinement.

Determination of Zone of Flow Instability in a Gas Flow Past a Square Particle in a Narrow Microchannel

The rapidly emerging industry of micro-electro-mechanical devices gives rise to new potential microfluidic applications. The analysis of the possible flow regimes is an important task of any microfluidic investigation. For a gas flow the transition between steady and unsteady regimes occurs at small Knudsen number Kn < 0.1 (Kn = l0 / L, where l0 is the mean free path of the gas molecules and L is the characteristic length). A continuum approach based on the Navier-Stokes-Fourier equations is applicable for this investigation. On the other side, the microfluidic application requires the problem to be investigated starting at very low Mach numbers (M = 0.1), close to incompressible regime. This makes pressure based methods very suitable for this investigation. The system of Navier-Stokes-Fourier equations is calculated numerically using pressure based algorithm SIMPLE-TS 2D. The results are validated by comparing them to data obtained by using molecular approach (direct simulation Monte Carlo (DSMC) method).

Strouhal number analysis for a Karman vortex gas flow past a square in a microchannel at low Mach number

The rapidly emerging industry of micro-electro-mechanical devices gives rise to new potential microfluidic applications. The analysis of the possible flow regimes is an important task of any microfluidic investigation. For unstable rarefied gas flows the transition between steady and unsteady regimes occurs at small Knudsen number Kn < 0.1 (Kn = l0/L, where l0 is the mean free path of the gas molecules and L is the characteristic length). The microfluidic problems include non-equilibrium effects to be taken into account. A continuum approach, based on the Navier-Stokes-Fourier equations with slip-velocity and jump-temperature boundary conditions, is applicable for this investigation. In this paper, we compare Strouhal number obtained from molecular (DSMC method) and continual (SIMPLE-TS algorithm) approach, for a flow past square in a microchannel at transition from steady to unsteady flow regime for a fixed Mach number (M = 0.4).

Modeling of gas flows through microchannel configurations

The present work is related to the study of the pressure driven isothermal gas flows through different microchannel configurations such as short straight micro-channels, 900 bend channels and T-shaped junctions. The direct simulation Monte Carlo (DSMC) method is used to calculate the gas flow through channel configurations in order to distinguish the flow regimes taking place in long and short microchannels. All the simulations were carried out in three dimensions but some of obtained results concern two dimensional configurations. In this case, the third dimension is confined between two specularly reflecting walls so that the flow in the third direction to be homogeneous. Implicit boundary conditions were applied to maintain a given pressure at inlet and outlet (I/O) boundaries. For small Knudsen number gas flow, the DSMC results are compared to the continuum numerical solution of the Navier-Stokes-Fourier equations obtained by using SIMPLE-TS finite volume method.

Influence of Reservoirs on Pressure Driven Gas Flow in a Microchannel

Rapidly emerging micro‐electro‐mechanical devices create new potential microfluidic applications. A simulation of an internal and external gas flows with accurate boundary conditions for these devices is important for their design. In this paper we study influence of reservoirs used at the microchannel inlet and outlet on the characteristics of the gas flow in the microchannel. The problem is solved by using finite volume method SIMPLE‐TS (continuum approach), which is validated using Direct Simulation Monte Carlo (molecular approach). We investigate two cases: a microchannels with reservoirs and without reservoirs. We compare the microchannels with different aspect ratios A = Lch/Hch =  10,15,20,30,40 and 50, where Lch is the channel length, Hch is the channel height. Comparisons of results obtained by using continuum approach for pressure driven flow in a microchannel with and without reservoirs at the channel ends are presented.

Unsteady State Gaseous Flow past a Square Confined in a Micro‐channel

Micro mechanical devices are rapidly emerging technology, where new potential applications are continuously being found. A simulation of internal and external gas flows in or around these devices is important for their design. The gas flows are characterized with areas of low speed flows (low Reynolds numbers). The flows can go from high speed supersonic to very low speed regimes down to the incompressible limit. This made the pressure based numerical methods very suitable to be used for calculation of this kind of gas flows. In this paper we present a short review of a finite volume method, developed by the authors, and demonstrate its application for calculation of some unsteady state gaseous flows. We study a flow past square‐shaped particle confined in a micro‐channel filled with a hard‐sphere monatomic gas. The problem is solved using the finite volume method SIMPLE‐TS (a modification of SIMPLE created by the authors). The flow motion is described on the basis of the Navier‐Stokes‐Fourier compressibl...