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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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, a streamline diffusion finite element method that is capable of balancing both the convection and the pressure, thus allowing the use of arbitrary pairs of velocity-pressure spaces is presented.
Abstract: For the Stokes equations with convection and the incompressible Navier–Stokes equations, the authors analyze a streamline diffusion finite element method that is capable of balancing both the convection and the pressure, thus allowing the use of arbitrary pairs of velocity-pressure spaces. For the linear problem, the authors obtain for all mesh–Peclet numbers optimal error estimates in natural norms including, in particular, the $L^2 $-norm of the pressure. The same holds for the nonlinear problem, which close to a regular branch of solutions, i.e., the linearized operator, is an isomorphism of the norm of the inverse of which still depends on the Reynolds number. Consequently, the dependence of the error constants on the Reynolds number is not completely resolved in this case.

126 citations

Journal ArticleDOI
TL;DR: The accuracy and the performance of three two-dimensional compressible flow codes at freestream Mach numbers as low as 0.001 are examined.
Abstract: The accuracy and the performance of three two-dimensional compressible flow codes at freestream Mach numbers as low as 0.001 are examined. Two of the codes employ a finite volume discretization scheme along with a multistage time-stepping algorithm to solve the Euler equations. The two codes differ in their respective use of cell-centered and node-centered differencing schemes. The third code uses an implicit finite difference procedure to solve the unsteady Navier-Stokes equations. Computational test cases are the inviscid steady flow over a circular cylinder and the impulsively started viscous flow over a cylinder

126 citations

Journal ArticleDOI
TL;DR: A new set of conservative 4th-order central finite differencing schemes for all the viscous terms of compressible Navier-Stokes equations are proposed and proved and used to simulate the vortex-induced oscillations of an elastically mounted circular cylinder.

126 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023183
2022389
2021544
2020509
2019545
2018575