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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Book•
16 Feb 2013
1,562 citations
TL;DR: In this article, an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid is presented. But the main idea is to incorporate Peskin's regularized delta function approach into a direct formulation of the fluid-solid interaction force in order to allow for a smooth transfer between Eulerian and Lagrangian representations.
1,399 citations
TL;DR: This paper shows that both of these effects of a non-Galilean invariance caused by a density-dependent coefficient in the convection term can be eliminated exactly in a lattice Boltzmann-equation model.
Abstract: It is known that the Frisch-Hasslacher-Pomeau lattice-gas automaton model and related models possess some rather unphysical effects. These are (1) a non-Galilean invariance caused by a density-dependent coefficient in the convection term, and (2) a velocity-dependent equation of state. In this paper, we show that both of these effects can be eliminated exactly in a lattice Boltzmann-equation model.
1,394 citations
Book•
01 Jan 1987
TL;DR: The second edition of the Navier-Stokes Equations as mentioned in this paper provides an overview of its application in a variety of problems, including the existence, uniqueness, and regularity of solutions.
Abstract: Preface to the second edition Introduction Part I. Questions Related to the Existence, Uniqueness and Regularity of Solutions: 1. Representation of a Flow: the Navier-Stokes Equations 2. Functional Setting of the Equations 3. Existence and Uniqueness Theorems (Mostly Classical Results) 4. New a priori Estimates and Applications 5. Regularity and Fractional Dimension 6. Successive Regularity and Compatibility Conditions at t=0 (Bounded Case) 7. Analyticity in Time 8. Lagrangian Representation of the Flow Part II. Questions Related to Stationary Solutions and Functional Invariant Sets (Attractors): 9. The Couette-Taylor Experiment 10. Stationary Solutions of the Navier-Stokes Equations 11. The Squeezing Property 12. Hausdorff Dimension of an Attractor Part III. Questions Related to the Numerical Approximation: 13. Finite Time Approximation 14. Long Time Approximation of the Navier-Stokes Equations Appendix. Inertial Manifolds and Navier-Stokes Equations Comments and Bibliography Comments and Bibliography Update for the Second Edition References.
1,342 citations
TL;DR: Improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods, and a new family of stiffly stable schemes is employed in mixed explicit/implicit time-intgration rules.
1,341 citations