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: The PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions and will be compared to the standard resolution technique, both in terms of CPU time and accuracy.
130 citations
TL;DR: A new and detailed analysis of the basic Uzawa algorithm for decoupling of the pressure and the velocity in the steady and unsteady Stokes operator is presented, focusing on explicit construction of the Uzawa pressure-operator spectrum for a semiperiodic model problem.
Abstract: A new and detailed analysis of the basic Uzawa algorithm for decoupling of the pressure and the velocity in the steady and unsteady Stokes operator is presented. The paper focuses on the following new aspects: explicit construction of the Uzawa pressure-operator spectrum for a semiperiodic model problem; general relationship of the convergence rate of the Uzawa procedure to classical inf-sup discretization analysis; and application of the method to high-order variational discretization.
130 citations
TL;DR: A review of the concept of a bulk viscosity coefficient β is presented in this paper, involving a discussion of theoretical approaches and a summary of existing experimental data, and issues related to using these data for dilatational flows in local thermodynamic equilibrium are addressed.
Abstract: A review of the concept of a bulk viscosity coefficient β is presented, involving a discussion of theoretical approaches and a summary of existing experimental data Two independent viscosity coefficients μ and A are obtained in the viscous stress tensor as a result of the isotropic Newtonian assumption Hence, all solutions of the Navier-Stokes equations must make an assumption regarding the functional form of A With β=λ+2/3μ by definition, the assumption is often arbitrarily made that the two viscosity coefficients are not independent, with β =0 This assumption has been shown to be valid only for dilute monatomic gases and is equivalent to stating that dilatational flowfield effects are not significant Theoretical approaches for quantifying β are classified according to whether the subject fluid is dilute or dense Experimental methods used to estimate bulk viscosity are described Existing experimental data are summarized for each fluid classification, and issues related to using these data for dilatational flows in local thermodynamic equilibrium are addressed
130 citations
TL;DR: It turns out that the two ROMs that utilize pressure modes are superior to the ROM that uses only velocity modes, both in terms of reproducing the results of the underlying simulations for obtaining the snapshots and of efficiency.
130 citations
09 Jun 1987
TL;DR: In this article, the influence of the upwind Euler discretization on the solution of the Navier-Stokes equations was investigated, like the type of upwind discretisation, the limiter and boundary formulation of the Euler fluxes, and the dependence of flux splitting on the total enthalpy.
Abstract: This paper is concerned with an investigation of the influence of the upwind Euler discretization on the solution of the Navier-Stokes equations. A number of elements of the upwind discretization were investigated, like the type of upwind discretization, the limiter and boundary formulation of the Euler fluxes, and the influence of flux splitting on the total enthalpy. Their influence on the accuracy of the viscous solution was demonstrated in test problems.
130 citations