Three-dimensional Rarefied Gas Flows Research Articles

A novel spatio-temporally adaptive parallel three-dimensional DSMC solver for unsteady rarefied micro/nano gas flows

An efficient parallel multi-scale direct simulation Monte Carlo algorithm to simulate three-dimensional rarefied gas flows over complex geometries is presented. The proposed algorithm employs a novel spatio-temporal adaptivity scheme. Based on the gradients of flow macro-properties, the spatio-temporal adaptivity scheme computes the cell size distribution and assigns the appropriate number of time sub-steps for each cell. The temporal adaptivity scheme provides local time step adaptation through different temporal levels employed in different cells. Spatial representation is based on a hierarchical octree Cartesian grid with low memory storage requirement. The hierarchical octree grid endows the method with straightforward and efficient data management suitable for particle ray tracing and dynamic grid refinement and coarsening. Solid objects, represented by triangulated surfaces, are incorporated using a cut-cell algorithm. A new parallelization scheme suitable for simulating strongly unsteady, non-equilibrium flows is proposed. The parallelization scheme, implemented for multi-core Central Processing Units (CPUs), significantly reduces the computational cost of modeling these flows. Performance of the method is assessed by comparing with benchmarked test cases for various rarefied gas flows.

Three-dimensional rarefied gas flows in constricted microchannels with different aspect ratios: asymmetry bifurcations and secondary flows

Results are presented of three-dimensional (3D) lattice Boltzmann method (LBM) simulation on pressure-driven rarefied gas flows through microchannels with a sudden contraction–expansion of 3:1:3. The main parameters examined are channel aspect ratio (AR) and Knudsen number (Kn o ) of 1–7 and 0.001–0.1, respectively. To cover the slip flow regime, a Bosanquet-type effective viscosity and a modified second-order slip boundary condition are used to account for the rarefaction effect on gas viscosity. The in-house 3D LBM code is verified by comparing the computed centerline streamwise pressure distribution and critical Reynolds number (Re c) of asymmetric bifurcation with experimental ones measured by others. The results are discussed in the way to explore effects of AR and Kn o on the bifurcation limits Re c of symmetric and asymmetric streamwise flows and effects of AR on the cross-sectional secondary flow patterns, which are lacking in the literature. Specifically, Re c for asymmetry bifurcation is found to first decrease linearly with increasing AR and then level off at 112 for AR > 3, whereas Re c decreases approximately linearly with increasing Kn o . Moreover, Re c can be correlated with AR and Kn o in a simple expression. The observed cross-sectional two- or four-pair counter-rotating vortices in the present rarefied laminar microchannel flows are new in terms of its absence in Newtonian laminar flows through straight micro- and macrochannels. Its driving force is the anisotropic secondary normal stresses over the cross-section as a result of the nonlinearity of the axial pressure gradient and, in turn, compressibility effect.

Construction and comparison of parallel implicit kinetic solvers in three spatial dimensions

The paper is devoted to the further development and systematic performance evaluation of a recent deterministic framework Nesvetay-3D for modelling three-dimensional rarefied gas flows. Firstly, a review of the existing discretization and parallelization strategies for solving numerically the Boltzmann kinetic equation with various model collision integrals is carried out. Secondly, a new parallelization strategy for the implicit time evolution method is implemented which improves scaling on large CPU clusters. Accuracy and scalability of the methods are demonstrated on a pressure-driven rarefied gas flow through a finite-length circular pipe as well as an external supersonic flow over a three-dimensional re-entry geometry of complicated aerodynamic shape.

Implicit multiblock method for solving a kinetic equation on unstructured meshes

A parallel multiblock implementation of a second-order accurate implicit numerical method based on solving a model kinetic equation is proposed for analyzing three-dimensional rarefied gas flows. The performance of the method is illustrated by computing test examples of gas flows in a circular pipe in a wide range of Knudsen numbers. The convergence rate and scalability of the method are analyzed depending on the number of blocks in the spatial grid.

Efficient Deterministic Modelling of Three-Dimensional Rarefied Gas Flows

AbstractThe paper is devoted to the development of an efficient deterministic framework for modelling of three-dimensional rarefied gas flows on the basis of the numerical solution of the Boltzmann kinetic equation with the model collision integrals. The framework consists of a high-order accurate implicit advection scheme on arbitrary unstructured meshes, the conservative procedure for the calculation of the model collision integral and efficient implementation on parallel machines. The main application area of the suggested methods is micro-scale flows. Performance of the proposed approach is demonstrated on a rarefied gas flow through the finite-length circular pipe. The results show good accuracy of the proposed algorithm across all flow regimes and its high efficiency and excellent parallel scalability for up to 512 cores.

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

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.

Implicit numerical method for computing three-dimensional rarefied gas flows on unstructured meshes

The method based on the numerical solution of a model kinetic equation is proposed for analyzing three-dimensional rarefied gas flows. The basic idea behind the method is the use of a second-order accurate TVD scheme on hybrid unstructured meshes in physical space and a fast implicit time discretization method without iterations at the upper level. The performance of the method is illustrated by computing test examples of three-dimensional rarefied gas flows in variously shaped channels in a wide range of Knudsen numbers.

Three-dimensional hypersonic rarefied gas flow round bodies of revolution

A proposed method of studying three-dimensional rarefied gas flow around a body of revolution is based on the numerical solution of model kinetic equations. By way of example, the problem is considered of hypersonic flow round an ellipsoid of revolution whose velocity vector forms an angle of α0 with the axis of symmetry of the body and is located in the plane of symmetry. A study is made of the effect of the angle of attack, surface temperature and Knudsen number on the aerodynamic characteristics of the body.