Showing papers on "Navier–Stokes equations published in 2014"
TL;DR: Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation element methods of arbitrary order for the compressible Navier--Stokes equations.
Abstract: Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation element methods of arbitrary order for the compressible Navier--Stokes equations. The new methods are similar to strong form, nodal discontinuous Galerkin spectral elements but conserve entropy for the Euler equations and are entropy stable for the Navier--Stokes equations. Shock capturing follows immediately by combining them with a dissipative companion operator via a comparison approach. Smooth and discontinuous test cases are presented that demonstrate their efficacy.
246 citations
TL;DR: In this paper, it was shown that the classical Cauchy problem for the incompressible 3D Navier-Stokes equations with (−1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times.
Abstract: We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (−1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.
174 citations
TL;DR: In this article, a meshless simulation method is presented for multiphase fluid-particle flows with a two-way coupled Smoothed Particle Hydrodynamics (SPH) for the fluid and the Discrete Element Method (DEM), for the solid phase.
152 citations
TL;DR: This article presents a new reduced order model based upon proper orthogonal decomposition (POD) for solving the Navier-Stokes equations that is a hybrid of two existing approaches, namely the quadratic expansion method and the Discrete Empirical Interpolation Method (DEIM).
146 citations
TL;DR: In this article, a new calibration case was introduced to the calibration procedure in order to achieve a better understanding of the variation of the resistance coefficients, and the coefficients were determined with a better description over the entire parameter space for the resistances than previously found in the literature.
142 citations
TL;DR: A new estimate of solutions for the Cauchy problem for the two-dimensional incompressible chemotaxis-Navier-Stokes equations is explored by taking advantage of a coupling structure of the equations and using a scale decomposition technique.
Abstract: In this paper, we investigate the Cauchy problem for the two-dimensional incompressible chemotaxis-Navier-Stokes equations. By taking advantage of a coupling structure of the equations and using a scale decomposition technique, we explore a new estimate of solutions. This estimate together with a microlocal analysis entails the global existence and uniqueness of weak solutions to the chemotaxis-Navier--Stokes system for a large class of initial data.
136 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
TL;DR: In this paper, a variational multiscale proper orthogonal decomposition (POD) reduced-order model for turbulent incompressible Navier-Stokes equations is presented.
Abstract: We develop a variational multiscale proper orthogonal decomposition (POD) reduced-order model (ROM) for turbulent incompressible Navier-Stokes equations. Under two assumptions on the underlying finite element approximation and the generation of the POD basis, the error analysis of the full discretization of the ROM is presented. All error contributions are considered: the spatial discretization error (due to the finite element discretization), the temporal discretization error (due to the backward Euler method), and the POD truncation error. Numerical tests for a three-dimensional turbulent flow past a cylinder at Reynolds number show the improved physical accuracy of the new model over the standard Galerkin and mixing-length POD ROMs. The high computational efficiency of the new model is also showcased. Finally, the theoretical error estimates are confirmed by numerical simulations of a two-dimensional Navier-Stokes problem. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 641–663, 2014
119 citations
TL;DR: This paper applies NURBS-based IGA to solve the fourth order stream function formulation of the Navier-Stokes equations, for which a priori error estimates for high order elliptic PDEs under h-refinement are derived.
01 Jan 2014
TL;DR: A simple finite-dimensional feedback control scheme for stabilizing solutions of infinite-dimensional dissipative evolution equations, such as reaction-diffusion systems, the Navier-Stokes equations and the Kuramoto-Sivashinsky equation is introduced.
Abstract: We introduce here a simple finite-dimensional feedback control scheme for stabilizing solutions of infinite-dimensional dissipative evolution equations, such as reaction-diffusion systems, the Navier-Stokes equations and the Kuramoto-Sivashinsky equation. The designed feedback control scheme takes advantage of the fact that such systems possess finite number of determining parameters (degrees of freedom), namely, finite number of determining Fourier modes, determining nodes, and determining interpolants and projections. In particular, the feedback control scheme uses finitely many of such observables and controllers. This observation is of a particular interest since it implies that our approach has far more reaching applications, in particular, in data assimilation. Moreover, we emphasize that our scheme treats all kinds of the determining projections, as well as, the various dissipative equations with one unified approach. However, for the sake of simplicity we demonstrate our approach in this paper to a one-dimensional reaction-diffusion equation paradigm.
TL;DR: This work considers the inverse problem of estimating the initial condition of a partial differential equation, which is observed only through noisy measurements at discrete time intervals, and adopts a Bayesian formulation resulting from a particular regularization that ensures the problem is well posed.
Abstract: We consider the inverse problem of estimating the initial condition of a partial differential equation, which is observed only through noisy measurements at discrete time intervals. In particular, ...
Book•
16 Sep 2014
TL;DR: In this article, Navier-Stokes Equations Behaviour Behaviour of L3-Norm has been studied for non-stationary energy solutions in Lemarie-Riesset Local Energy Solutions.
Abstract: Preliminaries Linear Stationary Problem Non-Linear Stationary Problem Linear Non-Stationary Problem Non-Linear Non-Stationary Problem Local Regularity Theory for Non-Stationary Navier-Stokes Equations Behaviour of L3-Norm Appendix A: Backward Uniqueness and Unique Continuation Appendix B: Lemarie-Riesset Local Energy Solutions
TL;DR: A new class of data is found for which the Prandtl boundary layer equations and the hydrostatic Euler equations are locally in time well-posed and the local existence and uniqueness hold.
Abstract: We find a new class of data for which the Prandtl boundary layer equations and the hydrostatic Euler equations are locally in time well-posed. In the case of the Prandtl equations, if the initial datum $u_0$ is monotone on a number of intervals (on some strictly increasing, on some strictly decreasing) and analytic on the complement of these intervals, we show that the local existence and uniqueness hold. The same result is true for the hydrostatic Euler equations if we assume these conditions for the initial vorticity $\omega_0=\partial_y u_0$.
TL;DR: In this article, large-eddy simulations of cavitating flow of a Diesel-fuel-like fluid in a generic throttle geometry are presented, where two-phase regions are modeled by a parameter-free thermodynamic equilibrium mixture model, and compressibility of the liquid and the liquid-vapor mixture is taken into account.
Abstract: Large-eddy simulations (LES) of cavitating flow of a Diesel-fuel-like fluid in a generic throttle geometry are presented. Two-phase regions are modeled by a parameter-free thermodynamic equilibrium mixture model, and compressibility of the liquid and the liquid-vapor mixture is taken into account. The Adaptive Local Deconvolution Method (ALDM), adapted for cavitating flows, is employed for discretizing the convective terms of the Navier-Stokes equations for the homogeneous mixture. ALDM is a finite-volume-based implicit LES approach that merges physically motivated turbulence modeling and numerical discretization. Validation of the numerical method is performed for a cavitating turbulent mixing layer. Comparisons with experimental data of the throttle flow at two different operating conditions are presented. The LES with the employed cavitation modeling predicts relevant flow and cavitation features accurately within the uncertainty range of the experiment. The turbulence structure of the flow is further analyzed with an emphasis on the interaction between cavitation and coherent motion, and on the statistically averaged-flow evolution.
TL;DR: This paper investigates numerically a diffuse interface model for the Navier–Stokes equation with fluid–fluid interface when the fluids have different densities and designs a C 0 finite element method and a special temporal scheme where the energy law is preserved at the discrete level.
TL;DR: In this article, a 3D numerical model has been developed to simulate dam-break flow over uneven beds in irregular domains, which solves the Reynolds-Averaged Navier-Stokes equations (RANS) using a finite-volume method based on collocated mesh that fits the solid boundaries such as bed and walls.
TL;DR: A new stabilized XFEM based fixed-grid approach for the transient incompressible Navier-Stokes equations using cut elements is developed, which is much more accurate and less sensitive to the location of the interface.
TL;DR: In this paper, the Navier-Stokes equation is used to describe fluid flow and solute transport through porous media, and the simulation results show that dispersion within the analyzed porous medium is adequately described by classical power laws obtained by analytic homogenization.
Abstract: In the present work fluid flow and solute transport through porous media are described by solving the governing equations at the pore scale with finite-volume discretization. Instead of solving the simplified Stokes equation (very often employed in this context) the full Navier-Stokes equation is used here. The realistic three-dimensional porous medium is created in this work by packing together, with standard ballistic physics, irregular and polydisperse objects. Emphasis is placed on numerical issues related to mesh generation and spatial discretization, which play an important role in determining the final accuracy of the finite-volume scheme and are often overlooked. The simulations performed are then analyzed in terms of velocity distributions and dispersion rates in a wider range of operating conditions, when compared with other works carried out by solving the Stokes equation. Results show that dispersion within the analyzed porous medium is adequately described by classical power laws obtained by analytic homogenization. Eventually the validity of Fickian diffusion to treat dispersion in porous media is also assessed.
TL;DR: In this article, the Lame system of linear elasticity and the fluid obeys the incompressible Navier-Stokes equations in a time-dependent domain is studied.
TL;DR: In this paper, a new hydrodynamic model for the interactions between collision-free Cucker-Smale flocking particles and a viscous incompressible fluid is presented.
Abstract: We present a new hydrodynamic model for the interactions between collision-free Cucker–Smale flocking particles and a viscous incompressible fluid. Our proposed model consists of two hydrodynamic models. For the Cucker–Smale flocking particles, we employ the pressureless Euler system with a non-local flocking dissipation, whereas for the fluid, we use the incompressible Navier–Stokes equations. These two hydrodynamic models are coupled through a drag force, which is the main flocking mechanism between the particles and the fluid. The flocking mechanism between particles is regulated by the Cucker–Smale model, which accelerates global flocking between the particles and the fluid. We show that this model admits the global-in-time classical solutions, and exhibits time-asymptotic flocking, provided that the initial data is appropriately small. In the course of our analysis for the proposed system, we first consider the hydrodynamic Cucker–Smale equations (the pressureless Euler system with a non-local flocking dissipation), for which the global existence and the time-asymptotic behavior of the classical solutions are also investigated.
TL;DR: This work analyzes the accuracy and conservation properties of two particular collocated and staggered schemes by solving various problems of Navier-Stokes equations.
Abstract: The Navier-Stokes equations describe fluid flow by conserving mass and momentum. There are two main mesh discretizations for the computation of these equations, the collocated and staggered schemes. Collocated schemes locate the velocity field at the same grid points as the pressure one, while staggered discretizations locate variables at different points within the mesh. One of the most important characteristic of the discretization schemes, aside from accuracy, is their capacity to discretely conserve kinetic energy, specially when solving turbulent flow. Hence, this work analyzes the accuracy and conservation properties of two particular collocated and staggered schemes by solving various problems.
TL;DR: In this paper, the authors study the long time, inviscid limit of the 2D Navier-Stokes equations near the periodic Couette flow, and confirm at the nonlinear level the qualitative behavior predicted by Kelvin's 1887 linear analysis at high Reynolds number Re.
Abstract: In this work we study the long time, inviscid limit of the 2D Navier-Stokes equations near the periodic Couette flow, and in particular, we confirm at the nonlinear level the qualitative behavior predicted by Kelvin's 1887 linear analysis At high Reynolds number Re, we prove that the solution behaves qualitatively like 2D Euler for times t \lesssim Re^(1/3), and in particular exhibits inviscid damping (eg the vorticity weakly approaches a shear flow) For times t \gtrsim Re^(1/3), which is sooner than the natural dissipative time scale O(Re), the viscosity becomes dominant and the streamwise dependence of the vorticity is rapidly eliminated by an enhanced dissipation effect Afterward, the remaining shear flow decays on very long time scales t \gtrsim Re back to the Couette flow When properly defined, the dissipative length-scale in this setting is L_D \sim Re^(-1/3), larger than the scale L_D \sim Re^(-1/2) predicted in classical Batchelor-Kraichnan 2D turbulence theory The class of initial data we study is the sum of a sufficiently smooth function and a small (with respect to Re^(-1)) $L^2$ function
TL;DR: In this article, a quasi-laminar stability approach is proposed to identify in high-Reynolds number flows the dominant low-frequencies and to design passive control means to shift these frequencies.
Abstract: This article presents a quasi-laminar stability approach to identify in high-Reynolds number flows the dominant low-frequencies and to design passive control means to shift these frequencies. The approach is based on a global linear stability analysis of mean-flows, which correspond to the time-average of the unsteady flows. Contrary to the previous work by Meliga et al. [“Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability,” Phys. Fluids 24, 061701 (2012)], we use the linearized Navier-Stokes equations based solely on the molecular viscosity (leaving aside any turbulence model and any eddy viscosity) to extract the least stable direct and adjoint global modes of the flow. Then, we compute the frequency sensitivity maps of these modes, so as to predict before hand where a small control cylinder optimally shifts the frequency of the flow. In the case of the D-shaped cylinder studied by Parezanovic and Cadot [J. Fluid Mech. 693, 115 (2012)], we show that the present approach we...
TL;DR: In this paper, the authors considered the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a general rigid bottom in a three-dimensional horizontally periodic setting.
Abstract: We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a general rigid bottom in a three-dimensional horizontally periodic setting. We establish the global well-posedness of the problem both with and without surface tension. We prove that without surface tension the solution decays to the equilibrium state at an almost exponential rate; with surface tension, we show that the solution decays at an exponential rate. Our results include the case in which a heavier fluid lies above a lighter one, provided that the surface tension at the free internal interface is above a critical value, which we identify. This means that sufficiently large surface tension stabilizes the Rayleigh–Taylor instability in the nonlinear setting. As a part of our analysis, we establish elliptic estimates for the two-phase stationary Stokes problem.
TL;DR: In this paper, the authors investigated the existence, uniqueness and regularity of stationary Stokes and Navier-Stokes problems in the Hilbert case and in L p -theory.
TL;DR: In this work, the wall boundary conditions are easily taken into account through a penalization technique, and the accuracy of the method is recovered using mesh adaptation, thanks to the potential of unstructured meshes.