Topic
Navier–Stokes equations
About: Navier–Stokes equations is a research topic. Over the lifetime, 18180 publications have been published within this topic receiving 552555 citations. The topic is also known as: Navier-Stokes equations.
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TL;DR: In this paper, a new class of splitting schemes for incompressible flows is introduced, based on a weak form of the pressure Poisson equation and, at each time step, only require to solve a set of Helmholtz-type equations for the velocity and a poisson equation (in the weak form) for the pressure.
153 citations
TL;DR: Three iterative methods for solving the stationary Navier–Stokes equations are considered, which are stability and convergence under the strong uniqueness conditions, where the iterative method II is the second order convergence.
152 citations
TL;DR: In this paper, the dynamics of thermocapillary flows in differentially heated cylindrical liquid bridges are investigated numerically using a mixed finite volume/pseudo-spectral method to solve the Navier-Stokes equations in the Boussinesq approximation.
Abstract: The dynamics of thermocapillary flows in differentially heated cylindrical liquid bridges is investigated numerically using a mixed finite volume/pseudo-spectral method to solve the Navier–Stokes equations in the Boussinesq approximation. For large Prandtl numbers (Pr = 4 and 7) and sufficiently high Reynolds numbers, the axisymmetric basic flow is unstable to three-dimensional hydrothermal waves. Finite-amplitude azimuthally standing waves are found to decay to travelling waves. Close to the critical Reynolds number, the former may persist for long times. Representative results are explained by computing the coefficients in the Ginzburg–Landau equations for the nonlinear evolution of these waves for a specific set of parameters. We investigate the nonlinear phenomena characteristic of standing and pure travelling waves, including azimuthal mean flow and time-dependent convective heat transport. For Pr [Lt ] 1 the first transition from the two-dimensional basic flow to the three-dimensional stationary flow is inertial in nature. Particular attention is paid to the secondary transition leading to oscillatory three-dimensional flow, and this mechanism is likewise independent of Pr. The spatial and temporal structure of the perturbation flow is analysed in detail and an instability mechanism is proposed based on energy balance calculations and the vorticity distribution.
152 citations
TL;DR: In this paper, the Navier-Stokes equations for gaseous slip flow in long microchannels with a second-order accurate slip boundary condition at the walls were analyzed.
152 citations
TL;DR: In this article, a meshless simulation method is presented for multiphase fluid-particle flows with a two-way coupled Smoothed Particle Hydrodynamics (SPH) for the fluid and the Discrete Element Method (DEM), for the solid phase.
152 citations