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: An automatic adaptive refinement technique has been coupled to the multigrid approach to produce an efficient and stable solution strategy for solving the steady-state incompressible Navier-Stokes equations.
216 citations
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TL;DR: The present numerical method is applied to both the forced motion and fluid-structure interaction problems and is able to solve fully coupled Navier-Stokes and dynamic equations for the moving body without introducing any iteration.
215 citations
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TL;DR: For the viscous and heat-conductive fluids governed by the Navier-Stokes equations with an external potential force, there exist non-trivial stationary solutions with zero velocity.
Abstract: For the viscous and heat-conductive fluids governed by the compressible Navier–Stokes equations with an external potential force, there exist non-trivial stationary solutions with zero velocity. By combining the Lp - Lq estimates for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the stationary profile in the whole space when the initial perturbation of the stationary solution and the potential force are small in some Sobolev norms. More precisely, the optimal convergence rates of the solution and its first order derivatives in L2-norm are obtained when the L1-norm of the perturbation is bounded.
215 citations
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TL;DR: It is shown that both ''conservative'' and ''consistent'' are important properties of the scheme to get an accurate result for high Hartmann number MHD flows with a strongly non-uniform mesh employed to resolve the Hartmann layers and side layers of Hunt's conductive walls and Shercliff's insulated walls.
215 citations
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TL;DR: In marginally resolved DNS and LES the new cubic skew-symmetric form represents a robust convective formulation which minimizes both aliasing and computational cost while also allowing a reduction in the use of computationally expensive high-order dissipative filters.
214 citations