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: In this paper, a second-order accurate method for solving viscous flow equations has been proposed that preserves conservation form, requires no block or scalar tridiagonal inversions, is simple and straightforward to program (estimated 10% modification for the update of many existing programs), and should easily adapt to current and future computer architectures.
Abstract: Although much progress has already been made In solving problems in aerodynamic design, many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely. This paper describes one such development. A new method for solving these equations has been devised that 1) is second-order accurate in space and time, 2) is unconditionally stable, 3) preserves conservation form, 4) requires no block or scalar tridiagonal inversions, 5) is simple and straightforward to program (estimated 10% modification for the update of many existing programs), 6) is more efficient than present methods, and 7) should easily adapt to current and future computer architectures. Computational results for laminar and turbulent flows at Reynolds numbers from 3 x 10(exp 5) to 3 x 10(exp 7) and at CFL numbers as high as 10(exp 3) are compared with theory and experiment.
326 citations
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01 May 2006TL;DR: The Navier-Stokes equations were established in the 19th century as the system of nonlinear partial differential equations which describe the motion of most commonly occurring fluids in air and water, and since that time exact solutions have been sought by scientists as mentioned in this paper.
Abstract: The Navier-Stokes equations were firmly established in the 19th Century as the system of nonlinear partial differential equations which describe the motion of most commonly occurring fluids in air and water, and since that time exact solutions have been sought by scientists. Collectively these solutions allow a clear insight into the behavior of fluids, providing a vehicle for novel mathematical methods and a useful check for computations in fluid dynamics, a field in which theoretical research is now dominated by computational methods. This 2006 book draws together exact solutions from widely differing sources and presents them in a coherent manner, in part by classifying solutions via their temporal and geometric constraints. It will prove to be a valuable resource to all who have an interest in the subject of fluid mechanics, and in particular to those who are learning or teaching the subject at the senior undergraduate and graduate levels.
325 citations
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TL;DR: In this paper, an analytical self-similar solution for the viscous flow in the spreading drop is obtained which satisfies the full Navier-Stokes equations, and an expression for the thickness of the boundary layer is used for the estimation of the residual film thickness formed by normal drop impact and the maximum spreading diameter.
Abstract: This study is devoted to a theoretical description of an unsteady laminar viscous flow in a spreading film of a Newtonian fluid. Such flow is generated by normal drop impact onto a dry substrate with high Weber and Reynolds numbers. An analytical self-similar solution for the viscous flow in the spreading drop is obtained which satisfies the full Navier–Stokes equations. The characteristic thickness of a boundary layer developed near the wall uniformly increases as a square root of time. An expression for the thickness of the boundary layer is used for the estimation of the residual film thickness formed by normal drop impact and the maximum spreading diameter. The theoretical predictions agree well with the existing experimental data. A possible explanation of the mechanism of formation of an uprising liquid sheet leading to splash is also proposed.
323 citations
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320 citations
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TL;DR: In this article, the Navier-Stokes equations that govern fluid flow are reduced to the more tractable Reynolds equation, which is valid for low Reynolds numbers and under certain restrictions on the magnitude of the roughness.
319 citations