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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01 Jan 1988
TL;DR: Navier-Stokes Equations as mentioned in this paper provide a compact and self-contained course on these classical, nonlinear, partial differential equations, which are used to describe and analyze fluid dynamics and the flow of gases.
Abstract: Both an original contribution and a lucid introduction to mathematical aspects of fluid mechanics, Navier-Stokes Equations provides a compact and self-contained course on these classical, nonlinear, partial differential equations, which are used to describe and analyze fluid dynamics and the flow of gases.
1,189 citations
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TL;DR: In this article, a geometric conservation law (GCL) is formulated that governs the spatial volume element under an arbitrary mapping and the GCL is solved numerically along with the flow conservation laws using conservative difference operators.
Abstract: Boundary-conforming coordinate transformations are used widely to map a flow region onto a computational space in which a finite-difference solution to the differential flow conservation laws is carried out. This method entails difficulties with maintenance of global conservation and with computation of the local volume element under time-dependent mappings that result from boundary motion. To improve the method, a differential ''geometric conservation law" (GCL) is formulated that governs the spatial volume element under an arbitrary mapping. The GCL is solved numerically along with the flow conservation laws using conservative difference operators. Numerical results are presented for implicit solutions of the unsteady Navier-Stokes equations and for explicit solutions of the steady supersonic flow equations.
1,188 citations
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TL;DR: In this paper, a numerical method for time dependent compressible Navier-Stokes equations applied to axisymmetric flow field produced by hypervelocity impact, examining viscous effects is presented.
Abstract: Numerical method for time dependent compressible Navier-Stokes equations applied to axisymmetric flow field produced by hypervelocity impact, examining viscous effects
1,156 citations
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04 Jun 1998
TL;DR: In this article, the Navier-Stokes equations and the Euler equations are studied in the context of nonlinear partial differential equations (NPDE) and their applications in applied mathematics.
Abstract: One of the most challenging topics in applied mathematics over the past decades has been the developent of the theory of nonlinear partial differential equations. Many of the problems in mechanics, geometry, probability, etc lead to such equations when formulated in mathematical terms. However, despite a long history of contributions, there exists no central core theory, and the most important advances have come from the study of particular equations and classes of equations arising in specific applications. This two volume work forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models. These models consist of systems of nonlinear partial differential equations like the incompressible and compressible Navier-Stokes equations. The main emphasis in Volume 1 is on the mathematical analysis of incompressible models. After recalling the fundamental description of Newtonian fluids, an original and self-contained study of both the classical Navier-Stokes equations (including the inhomogenous case) and the Euler equations is given. Known results and many new results about the existence and regularity of solutions are presented with complete proofs. The discussion containts many interesting insights and remarks. The text highlights in particular the use of modern analytical tools and methods and also indicates many open problems.
1,149 citations
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TL;DR: On developpe un schema de relaxation multigrille, application a des ecoulements transsoniques d'application a des Ecoulements Transsoniques.
Abstract: On developpe un schema de relaxation multigrille. Application a des ecoulements transsoniques
1,131 citations