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Dissipative Particle Dynamics (DPD) has, with only a few exceptions, been used to study hydrodynamic behavior of complex fluids without confinement. Previous studies used a periodic boundary condition, and only bulk behavior can be studied effectively. However, if solid walls play an important role in the problem to be studied, a no-slip boundary condition in DPD is required. Until now the methods used to impose a solid wall consisted of a frozen layer of particles. If the wall density is equal to the density of the simulated domain, slip phenomena are observed. To suppress this slip, the density of the wall has to be increased. We introduce a new method, which intrinsically imposes the no-slip boundary condition without the need to artificially increase the density in the wall. The method is tested in both a steady-state and an instationary calculation. If repulsion is applied in frozen particle methods, density distortions are observed. We propose a method to avoid these distortions. Finally, this method is tested against conventional computational fluid dynamics (CFD) calculations for the flow in a lid-driven cavity. Excellent agreement between the two methods is found.

The 13-speed thermal lattice Bhatnagar–Gross–Krook model on hexagonal lattice is a single relaxation time model with an adjustable parameter λ which makes the Prandtl number tunable. This model maintains the simplicity of the lattice Boltzmann method (LBM) and is also suitable for various thermal fluids. In this paper, it is applied to simulations of the lid-driven flow in a square cavity at a wide range of Reynolds numbers. Numerical experiments show that this model can give the same accurate results as those by the conventional numerical methods.

The regularized lattice BGK (RLBGK) is validated against high-accuracy spectral Chebyshev methods for lid-driven cavity flows. RLBGK is shown to provide a viable alternative to standard lattice BGK schemes, with significant enhancement of numerical stability at a very moderate computational extra-cost.

The flows around a typical open cavity with a store are numerically simulated in this paper. A fully implicit unfactored method is employed in the solver of RANS equations, where the S-A turbulent model is implemented to calculate the turbulent eddy viscosity. The flow-induced oscillation of the free shear layer around the cavity lip is captured and analyzed. Comparisons for the different cases of the cavity flow are made. The calculated results show that the pressure fluctuation is pertinent to the different positions of the store inside the cavity. The power spectral density (PSD) of the pressure by fast Fourier transformations (FFT) is also displayed in the paper. For the Rossiter's oscillatory mode, the numerical results compare well with the experimental data.

The enhancement of the heat transfer of fluids is a very important task in engineering and technology which can be accomplished through the hybrid nanoparticles. In this theoretical investigation, the natural convection flow of nanoliquid through a square container is examined under the impacts of thermal boundary conditions. The considered nanoliquid is a combination of titanium alloy Ti6Al4V (class of titanium) and aluminum alloy AA7075 (class of aluminum) nanoparticles and water as a base fluid. Aluminum alloys are commonly used in household wiring and manufacturing of wheels, etc. The titanium alloy Ti6Al4V is commonly acknowledged as the “workhorse” of titanium which is extensively used in aerospace and biomedical engineering. The mathematical model is developed in the form of nonlinear partial differential equations and later transformed into dimensionless form. The resultant dimensionless set of equations is simulated numerically by using the eminent finite element method (FEM). The iterative Newton’s Raphson method is used to get the optimal solutions. The stream function and temperature contours are displayed against the Rayleigh number and nanoparticle volume friction. The variation of local and average Nusselt numbers is also plotted. The outcomes revealed that water-based titanium alloy is the best choice to enhance the heat transfer rate in the cavity. The results obtained in this investigation are very important in engineering research, academic, and discussion about the heat transfer analysis with these two types of alloy nanoparticles inside the cavity flows.

A benchmark problem with air medium in a square cavity heated by a vertical side is studied in a Ra range near its critical value without using the usual model approximations, such as Boussinesq or low-Mach-number approximation. Two analysis methods of power spectrum and phase trajectory are adopted to distinguish the flow pattern in the cavity. It demonstrates how the flow evolves from transition to turbulent regimes with increasing Ra values.

In this work mesh-free method is used for solving two dimensional lid-driven cavity flow in a wide range of Reynolds numbers. The algorithm of mesh-free characteristic based split has been employed for this purpose. The results obtained from mesh-free characteristic based split algorithm have been compared to those of the finite element. The effect of using different shape functions on accuracy and stability of solution has been discussed. The sensitivity of stability of solution to nodes irregularity has been investigated. The effects of number of Gaussian integration points on the accuracy have been discussed.

In this paper, a fourth-order compact stencil finite difference scheme is developed for solving elliptic Poisson equation. The scheme presented here is based on a modular approach using a linear combination of compact difference algorithms that results in different discrete formulation than the well-known Mehrstellen scheme. An adjoint optimal V-cycle multigrid (MG) iterative solver are developed, implemented, and tested. The robustness of the adjoint Poisson solver is illustrated by solving incompressible Navier–Stokes equations in vorticity-stream function formulation. Using a fully implicit factorized delta-scheme algorithm for the time integration, benchmark quality results of the cavity flow problem are presented and compared to existing literature for various Reynolds numbers.