Volume 40, Issue 4

A two-level parallelization algorithm is proposed for the direct simulation Monte Carlo (DSMC) method. The algorithm is based on the decomposition of the computational domain into subdomains, which in turn are divided into blocks. The algorithm is implemented in the DSMC software code using MPI and OpenMP technologies. The algorithm was tested on the problem of spherical gas expansion into a vacuum from an evaporating surface, which is of interest for astrophysical applications. The problem is characterized both by large gradients of physical parameters and large time of stationary solution achievement. The calculations were carried out on the resources of the Polytechnic – RSK Tornado supercomputer. When solving the problem, OpenMP technology is used to calculate blocks of subdomain by single process associated with single node, each containing 28 threads with shared memory. MPI technology is used to exchange data on migrating between subdomains particles among nodes with distributed memory. The speedup of the algorithm was 35 on 64 nodes of the supercomputer. Additionally, a single-level decomposition algorithm was tested, implemented only by MPI tools both for calculating subdomains within them. The high efficiency of the single-level algorithm for a relatively small number of threads is shown. The boundary of the preferred use of the two-level algorithm is defined.

The aim of this work is the substantiation of the applicability of the splitting scheme to the solution of reactive transport in porous media problems involving precipitation–dissolution reactions and variable media porosity. The reasons why this scheme was abandoned for modelling this type of problems in the previous works are analyzed. We consider a corrected scheme featuring mass conservation and convergence. It is tested on problems with analytical solutions and its performance is shown on a benchmark of the dissolution of concrete minerals.

The problems of numerical modelling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier–Stokes equations exist at large Reynolds numbers, but they are unstable and lead to transient or turbulent unsteady regimes. In addition, the solution of the boundary value problem at large values of Reynolds number may be non-unique. In this paper, we consider numerical algorithms for finding such stationary solutions. We use natural pressure-velocity variables under standard finite element approximation on triangular grids. Iterative methods with different linearizations of convective transport are used to test a two-dimensional problem of incompressible fluid flow in a square-section cavity with a movable top lid. The developed computational algorithm allowed us to obtain two solutions when the Reynolds number exceeds a critical value for flows in a cavity of semi-elliptical cross-section.

In this work we propose an extension of the low-rank Monte Carlo algorithm for modelling aggregation process with multiple sources of particles. This implementation utilizes the low-rank structure of the coagulation kernel and reduces the number of operations for selection of pairs of coagulating particles. This approach does not require the kernel itself to be low-rank or to have such an approximation. Instead, it is sufficient to use an auxiliary low-rank kernel as a majorant function. We demonstrate the convergence of our method using the known theoretical solutions and show an agreement of the numerical particle size distributions with the results obtained by the deterministic numerical method. In addition, we analyze the performance of the Monte Carlo method for a simplified system with active monomers and collisional shattering events. We remind that numerical modelling based on relatively small number of finite samples can deviate from analytical solution of the kinetic equations.

The paper describes the numerical methods and the associated parallel computing code ‘Gerbera’ designed to analyse the aerodynamics and tonal noise of arbitrary aircraft propeller systems. The capabilities, robustness and accuracy of ‘Gerbera’ are demonstrated on a series of validation and verification studies, including single propellers, distributed propellers, and contra-rotating open rotor. The correct calculation of the propeller thrust characteristics and the main noise harmonics, including quite ‘subtle’ interaction effects, is shown. The presented scalability tests confirm good speed-up up to thousands of CPU cores.