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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.


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TL;DR: The method of manufactured solutions is used to verify the order of accuracy of two finite‐volume Euler and Navier–Stokes codes, giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised.
Abstract: The method of manufactured solutions is used to verify the order of accuracy of two finite-volume Euler and Navier–Stokes codes. The Premo code employs a node-centred approach using unstructured meshes, while the Wind code employs a similar scheme on structured meshes. Both codes use Roe's upwind method with MUSCL extrapolation for the convective terms and central differences for the diffusion terms, thus yielding a numerical scheme that is formally second-order accurate. The method of manufactured solutions is employed to generate exact solutions to the governing Euler and Navier–Stokes equations in two dimensions along with additional source terms. These exact solutions are then used to accurately evaluate the discretization error in the numerical solutions. Through global discretization error analyses, the spatial order of accuracy is observed to be second order for both codes, thus giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised. Examples of coding mistakes discovered using the method are also given. Copyright © 2004 John Wiley & Sons, Ltd.

173 citations

Journal ArticleDOI
TL;DR: In this paper, the flow in a laminar separation bubble is analyzed by means of finite-difference solutions to the Navier-Stokes equations for incompressible flow.
Abstract: The flow in a two-dimensional laminar separation bubble is analyzed by means of finite-difference solutions to the Navier-Stokes equations for incompressible flow. The study was motivated by the need to analyze high-Reynolds-number flow fields having viscous regions in which the boundary-layer assumptions are questionable. The approach adopted in the present study is to analyze the flow in the immediate vicinity of the separation bubble using the Navier-Stokes equations. It is assumed that the resulting solutions can then be patched to the remainder of the flow field, which is analyzed using boundary-layer theory and inviscid-flow analysis. Some of the difficulties associated with patching the numerical solutions to the remainder of the flow field are discussed, and a suggestion for treating boundary conditions is made which would permit a separation bubble to be computed from the Navier-Stokes equations using boundary conditions from inviscid and boundary-layer solutions without accounting for interaction between individual flow regions. Numerical solutions are presented for separation bubbles having Reynolds numbers (based on momentum thickness) of the order of 50. In these numerical solutions, separation was found to occur without any evidence of the singular behaviour at separation found in solutions to the boundary-layer equations. The numerical solutions indicate that predictions of separation by boundary-layer theory are not reliable for this range of Reynolds number. The accuracy and validity of the numerical solutions are briefly examined. Included in this examination are comparisons between the Howarth solution of the boundary-layer equations for a linearly retarded freestream velocity and the corresponding numerical solutions of the Navier-Stokes equations for various Reynolds numbers.

173 citations

Journal ArticleDOI
TL;DR: In this paper, the proper orthogonal decomposition (POD) approach is applied to the case of multiple parameters in the context of a class of reduced-order models.

173 citations

Journal ArticleDOI
TL;DR: In this article, the asymptotic analysis of a system of coupled kinetic and fluid equations, namely the Vlasov-Fokker-Planck equation and a compressible Navier-Stokes equation, is studied.
Abstract: This article is devoted to the asymptotic analysis of a system of coupled kinetic and fluid equations, namely the Vlasov-Fokker-Planck equation and a compressible Navier-Stokes equation Such a system is used, for example, to model fluid-particle interactions arising in sprays, aerosols or sedimentation problems The asymptotic regime corresponding to a strong drag force and a strong Brownian motion is studied and the convergence toward a two phase macroscopic model is proved The proof relies on a relative entropy method

173 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider 3D Euler and Navier-Stokes equations describing dynamics of uniformly rotating fluids and show that solutions of these equations can be decomposed as U(t, x1, x2, x3) + r, where r is a solution of the 2D NN system with vertically averaged initial data (axis of rotation is taken along the vertical e3).
Abstract: We consider 3D Euler and Navier–Stokes equations describing dynamics of uniformly rotating fluids. Periodic (as well as zero vertical flux) boundary conditions are imposed, the ratios of domain periods are assumed to be generic (nonresonant). We show that solutions of 3D Euler/Navier–Stokes equations can be decomposed as U(t, x1, x2, x3) = Ũ(t, x1, x2) +V(t, x1, x2, x3) + r, where Ũ is a solution of the 2D Euler/Navier–Stokes system with vertically averaged initial data (axis of rotation is taken along the vertical e3). The vector field V(t, x1, x2, x3) is exactly solved in terms of the phases Ωt, τ1(t) and τ2(t). The phases τ1(t) and τ2(t) explicitly expressed in terms of vertically averaged vertical vorticity curl U(t) ·e3 and velocity U 3 (t). The remainder r is uniformly estimated from above by a majorant of order a3/Ω, a3 is the vertical aspect ratio (shallowness) and Ω is non-dimensional rotation parameter based on horizontal scales. The resolution of resonances and a non-standard small divisor problem for 3D rotating Euler are the basis for error estimates. Contribution of 3-wave resonances is estimated in terms of the measure of almost resonant aspect ratios. Global solvability of the limit equations and estimates of the error r are used to prove existence on a long time interval T ∗ of regular solutions to 3D Euler equations (T ∗ → +∞, as 1/Ω → 0); and existence on infinite time interval of regular solutions to 3D Navier–Stokes equations with smooth arbitrary initial data in the case of small 1/Ω.

172 citations


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