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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: In this article, numerical simulations on a self-propelled fish-like body were performed using the Reynolds-Averaged-Navier-Stokes Equations (RANSAC).
115 citations
TL;DR: In this paper, the velocity gradient tensor satisfies the nonlinear evolution equation (dAij/dt)+AikAkj−1/3 (AmnAnm)δij=Hij where Aij=∂ui/∂xj and the tensor Hij contains terms involving the action of cross derivatives of the pressure field and viscous diffusion of Aij.
Abstract: Studies of direct numerical simulations of incompressible, homogeneous, and inhomogeneous turbulence indicate that, in regions of high kinetic energy dissipation rate, the geometry of the local velocity gradient field has a universal character. The velocity gradient tensor satisfies the nonlinear evolution equation (dAij/dt)+AikAkj−1/3 (AmnAnm)δij=Hij where Aij=∂ui/∂xj and the tensor Hij contains terms involving the action of cross derivatives of the pressure field and viscous diffusion of Aij. The restricted Euler equation corresponding to Hij=0 can be solved in closed form [Cantwell, Phys. Fluids A 4, 782 (1992)] and the solution has the property that, for any initial condition, Aij(t) evolves to an asymptotic state of the form Aij(t)≂Kij[R(t)]1/3 where R(t) is a function which becomes singular in a finite time and Kij is a constant matrix. A number of the universal features of fine‐scale motions observed in direct numerical simulations are reproduced by Kij.In the simulation studies the first invariant...
115 citations
TL;DR: An overview of the Trefftz finite element and its application in various engineering problems can be found in this article, where a modified variational functional and T-complete solutions of the Lame-Navier equations are derived for the in-plane intraelement displacement field.
Abstract: This paper presents an overview of the Trefftz finite element and its application in various engineering problems. Basic concepts of the Trefftz method are discussed, such as T-complete functions, special purpose elements, modified variational functionals, rank conditions, intraelement fields, and frame fields. The hybrid-Trefftz finite element formulation and numerical solutions of potential flow problems, plane elasticity, linear thin and thick plate bending, transient heat conduction, and geometrically nonlinear plate bending are described. Formulations for all cases are derived by means of a modified variational functional and T-complete solutions. In the case of geometrically nonlinear plate bending, exact solutions of the Lame-Navier equations are used for the in-plane intraelement displacement field, and an incremental form of the basic equations is adopted. Generation of elemental stiffness equations from the modified variational principle is also discussed. Some typical numerical results are presented to show the application of the finite element approach. Finally, a brief summary of the approach is provided and future trends in this field are identified. There are 151 references cited in this revised article. DOI: 10.1115/1.1995716
114 citations
TL;DR: In this article, high accuracy finite difference approximations were developed for partial differential equations of elliptic type, with particular emphasis on the convection-diffusion equation, and they were extended to the solution of Navier-Stokes equations.
114 citations
TL;DR: This paper presents the latest developments of a discontinuous Galerkin (DG) method for incompressible flows introduced in [Bassi F, Crivellini A, Di Pietro DA, Rebay S] to the coupled Navier–Stokes and energy equations governing natural convection flows and a review of the method together with two recently developed issues.
114 citations