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: Bresch et al. as discussed by the authors investigated the global in time existence of sequences of weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids.
280 citations
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TL;DR: In this article, the Navier-Stokes equations are solved with exact solutions for two-and three-dimensional shear flows of unbounded extent, including two-dimensional stagnation point flows and 2-dimensional flows with uniform vorticity.
Abstract: New classes of exact solutions of the incompressible Navier-Stokes equations are presented. The method of solution has its origins in that first used by Kelvin (Phil. Mag. 24 (5), 188-196 (1887)) to solve the linearized equations governing small disturbances in unbounded plane Couette flow. The new solutions found describe arbitrarily large, spatially periodic disturbances within certain two- and three-dimensional 'basic' shear flows of unbounded extent. The admissible classes of basic flow possess spatially uniform strain rates; they include two- and three-dimensional stagnation point flows and two-dimensional flows with uniform vorticity. The disturbances, though spatially periodic, have time-dependent wavenumber and velocity components. It is found that solutions for the disturbance do not always decay to zero; but in some instances grow continuously in spite of viscous dissipation. This behaviour is explained in terms of vorticity dynamics.
280 citations
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TL;DR: In this article, a discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids, where the governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model.
Abstract: A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplyfying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.
279 citations
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TL;DR: A physically consistent phase-field model that admits an energy law is proposed, and several energy stable, efficient, and accurate time discretization schemes for the coupled nonlinear phase- field model are constructed and analyzed.
Abstract: Modeling and numerical approximation of two-phase incompressible flows with different densities and viscosities are considered. A physically consistent phase-field model that admits an energy law is proposed, and several energy stable, efficient, and accurate time discretization schemes for the coupled nonlinear phase-field model are constructed and analyzed. Ample numerical experiments are carried out to validate the correctness of these schemes and their accuracy for problems with large density and viscosity ratios.
279 citations
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TL;DR: It is shown that with certain choices of the velocity interpolation, unstructured staggered mesh discretizations of the divergence form of the Navier?Stokes equations can conserve kinetic energy and momentum both locally and globally.
277 citations