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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14 Jan 1985
310 citations
TL;DR: The spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier-Stokes equations are explained in detail and implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed.
Abstract: SUMMARY The spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier-Stokes equations are explained in detail. The concept of pressure modes, physical and spurious, pure and impure, is introduced and their effects on discretized solutions is analysed, in the context of both mixed interpolation and penalty approaches. Pressure filtering schemes, which are capable of recovering useful pressures from otherwise polluted numerical results, are developed for two particular elements in two-dimensions and one element in three-dimensions. The automatic pressure filter associated with the penalty method is also explained. Implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed and a list of unanswered questions presented. Sufficient numerical examples are discussed to corroborate the theory presented herein.
309 citations
TL;DR: In this paper, a criterion of local Holder continuity for suitable weak solutions to Navier-Stokes equations is presented. But the main part of the proof is based on a blow-up procedure and can be applied to other problems in spaces of solenoidal vector fields.
Abstract: We prove a criterion of local Holder continuity for suitable weak solutions to the Navier—Stokes equations. One of the main part of the proof, based on a blow-up procedure, has quite general nature and can be applied to other problems in spaces of solenoidal vector fields.
309 citations
TL;DR: In this paper, the Navier-Stokes and energy equations were solved using an elliptic numerical procedure for a horizontal isothermal cylinder, and the flow approach natural convection from a line heat source as Ra → 0 and laminar boundary-layer flow as Ra→ ∞.
308 citations
TL;DR: It is shown on a variety of problems that the most cost-effective simulations can be obtained using higher-order basis functions when compared with the traditional linear basis.
Abstract: Stabilized finite element methods have been shown to yield robust, accurate numerical solutions to both the compressible and incompressible Navier-Stokes equations for laminar and turbulent flows. The present work focuses on the application of higher-order, hierarchical basis functions to the incompressible Navier-Stokes equations using a stabilized finite element method. It is shown on a variety of problems that the most cost-effective simulations (in terms of CPU time, memory, and disk storage) can be obtained using higher-order basis functions when compared with the traditional linear basis. In addition, algorithms will be presented for the efficient implementation of these methods within the traditional finite element data structures
308 citations