Showing papers on "Navier–Stokes equations published in 2020"
TL;DR: The work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields, respectively.
99 citations
TL;DR: The framework of inner product norm preserving relaxation Runge-Kutta methods is extended to general convex quantities and is proved analytically and demonstrated in several numerical examples, including applications to high-order entropy-conservative and entropy-stable semi-discretizations on unstructured grids for the compressible Euler and Navier-Stokes equations.
Abstract: The framework of inner product norm preserving relaxation Runge--Kutta methods [D. I. Ketcheson, SIAM J. Numer. Anal., 57 (2019), pp. 2850--2870] is extended to general convex quantities. Conservat...
89 citations
TL;DR: Computational fluid dynamics through the solution of the Navier–Stokes equations with turbulence models has become commonplace, but simply solving these equations is not sufficient to be able to solve the turbulence models.
Abstract: Computational fluid dynamics through the solution of the Navier–Stokes equations with turbulence models has become commonplace. However, simply solving these equations is not sufficient to be able ...
88 citations
TL;DR: In this paper, the authors show that the Navier-Stokes equations are stable and causal if one adopts suitable non-equilibrium definitions of the hydrodynamic variables: temperature, fluid velocity, and the chemical potential.
Abstract: Relativistic Navier-Stokes equations express the conservation of the energy-momentum tensor and the particle number current in terms of the local hydrodynamic variables: temperature, fluid velocity, and the chemical potential. We show that the viscous-fluid equations are stable and causal if one adopts suitable non-equilibrium definitions of the hydrodynamic variables.
76 citations
TL;DR: The fully parabolic Keller--Segel system is coupled to the incompressible Navier--Stokes equations through transport and buoyancy and it is shown that when posed with no-flux/no-Flux/Dirichlet boundar...
Abstract: The fully parabolic Keller--Segel system is coupled to the incompressible Navier--Stokes equations through transport and buoyancy. It is shown that when posed with no-flux/no-flux/Dirichlet boundar...
58 citations
TL;DR: In this article, the Nernst-Planck equation and Poisson's equation together with the traditional Navier Stokes equations are simulated for the conservation of ionic species.
44 citations
TL;DR: An efficient numerical scheme based on the scalar auxiliary variable (SAV) and marker and cell scheme (MAC) is constructed for the Navier-Stokes equations to show that both velocity and pressure approximations are second-order accurate in time and space.
Abstract: An efficient numerical scheme based on the scalar auxiliary variable (SAV) and marker and cell (MAC) scheme is constructed for the Navier--Stokes equations. A particular feature of the scheme is th...
44 citations
05 Jun 2020
TL;DR: In this paper, the authors studied the regularity of weak solutions to the incompressible Boussinesq equations in R 3 × (0, T ). The main goal of the paper was to establish a regularity criterion in terms of one velocity component and the gradient of temperature in Lorentz spaces.
Abstract: In this paper, we study the regularity of weak solutions to the incompressible Boussinesq equations in R 3 × ( 0 , T ) . The main goal is to establish the regularity criterion in terms of one velocity component and the gradient of temperature in Lorentz spaces.
42 citations
40 citations
TL;DR: In this paper, the authors considered the numerical approximation of the flow-coupled phase-field model of two-phase incompressible flows using the mass-conserved Allen-Cahn equation.
Abstract: Funding information NSF-DMS, Grant/Award Numbers: 1720212, 1818783, 2012490 Abstract We consider the numerical approximation of the flow-coupled phase-field model of two-phase incompressible flows using the mass-conserved Allen-Cahn equation. Due to the highly nonlinear nature of the coupling, how to develop an accurate and practically efficient scheme has always been a challenging problem. To solve this challenge, we construct a novel effective fully decoupled scheme that is linear, unconditional energy stable, and second-order time accurate. The key idea of decoupling is to introduce a nonlocal variable and a related ordinary differential equation to deal with the nonlinear coupling terms that satisfy the so-called “zero-energy-contribution” property. Thus, in actual calculations, this scheme only needs to solve several independent linear equations at each time step to obtain a numerical solution with the second-order time accuracy. We strictly prove the solvability and unconditional energy stability and perform numerical simulations in 2D and 3D to verify the accuracy and stability of the scheme numerically.
40 citations
TL;DR: In this article, a compatible model to deal with the impacts of two nanoparticles like SWCNT and MWCNT within the base fluid pure water under the considrertion, developed the mathematical model and applied the boundary layer approximation on the Navier Stokes equations.
Abstract: In this study, heat transfer of CNTs base micropolar fluid flow over a Riga plate The effects of thermal slip and velocity slip considred to analyze at Riga plate The compatible model to deals with the impacts of two nanoparticles like SWCNT and MWCNT within the base fluid pure water Under the considrertion, we developed the mathematical model and applied the boundary layer approximation on the Navier Stokes equations the dimensionless model have been solve through numerical methos via Maple Software The involving dimensionless parameters effects are presented in the form of tables and graphs Surpringly, the best achievement in the heat transfer rate and boundary layer thickness gain by MWCNT as compared to SWCNT
TL;DR: In this paper, it was shown that the existence of non-unique weak solutions for the 3D Navier-Stokes equations with fractional hyperviscosity is known whenever the exponent of the Navier−Stokes equation is less than the Lions' exponent 5/4.
Abstract: Using the convex integration technique for the three-dimensional Navier–Stokes equations introduced by Buckmaster and Vicol, it is shown the existence of non-unique weak solutions for the 3D Navier–Stokes equations with fractional hyperviscosity $$(-\Delta )^{\theta }$$, whenever the exponent $$\theta $$ is less than Lions’ exponent 5/4, i.e., when $$\theta < 5/4$$.
TL;DR: In this article, the vorticity form of the 2D Euler equations is considered and the stationary solutions of this equation converge to the unique stationary solution of the Navier-Stokes equation driven by the space-time white noise.
Abstract: We consider the vorticity form of the 2D Euler equations which is perturbed by a suitable transport type noise and has white noise initial condition. It is shown that stationary solutions of this equation converge to the unique stationary solution of the 2D Navier–Stokes equation driven by the space-time white noise.
TL;DR: In this paper, a parametric, hybrid reduced order method based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented.
TL;DR: In this article, the authors extend the resolvent formalism for wall turbulence to account for the effect of streamwise-constant riblets, and the Navier-Stokes equations are interpreted under this formulation.
Abstract: This paper extends the resolvent formalism for wall turbulence to account for the effect of streamwise-constant riblets. Under the resolvent formulation, the Navier–Stokes equations are interpreted...
TL;DR: In this paper, the inviscid limit for the Navier-Stokes equations in a half space, with initial datum that is analytic only close to the boundary of the domain, and that has Sobolev regularity in the complement, was studied.
Abstract: We address the inviscid limit for the Navier–Stokes equations in a half space, with initial datum that is analytic only close to the boundary of the domain, and that has Sobolev regularity in the complement. We prove that for such data the solution of the Navier–Stokes equations converges in the vanishing viscosity limit to the solution of the Euler equation, on a constant time interval.
TL;DR: In this paper, a viscous incompressible fluid evolving within a smooth bounded domain, either in 2D or in 3D, is considered and the boundary controls are only located on a small part of the boundary, intersecting all its connected components.
Abstract: In this work, we investigate the small-time global exact controllability of the Navier-Stokes equation , both towards the null equilibrium state and towards weak trajectories. We consider a viscous incompressible fluid evolving within a smooth bounded domain, either in 2D or in 3D. The controls are only located on a small part of the boundary, intersecting all its connected components. On the remaining parts of the boundary, the fluid obeys a Navier slip-with-friction boundary condition. Even though viscous boundary layers appear near these uncontrolled boundaries, we prove that small-time global exact controllability holds. Our analysis relies on the controllability of the Euler equation combined with asymptotic boundary layer expansions. Choosing the boundary controls with care enables us to guarantee good dissipation properties for the residual boundary layers, which can then be exactly canceled using local techniques.
TL;DR: In this paper, the existence of global weak discretely self-similar solutions to the Navier-Stokes equations with locally square integrable initial velocities was shown.
Abstract: We show the existence of global weak solutions to the three dimensional Navier–Stokes equations with initial velocity in the weighted spaces $$L^2_{w_\gamma }$$, where $$w_\gamma (x)=(1+\vert x\vert )^{-\gamma }$$ and $$0<\gamma \leqq 2$$, using new energy controls. As an application we give a new proof of the existence of global weak discretely self-similar solutions to the three dimensional Navier–Stokes equations for discretely self-similar initial velocities which are locally square integrable.
TL;DR: Mohamed et al. as discussed by the authors proposed a Discrete Exterior Calculus (DEC) discretization of Navier-Stokes equations over simplicial meshes, which preserves the stationary state, and conserves the inviscid invariants over an extended period of time.
Abstract: A conservative primitive variable discrete exterior calculus (DEC) discretization of the Navier-Stokes equations is performed. An existing DEC method (Mohamed, M. S., Hirani, A. N., Samtaney, R. (2016). Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes. Journal of Computational Physics, 312, 175-191) is modified to this end, and is extended to include the energy-preserving time integration and the Coriolis force to enhance its applicability to investigate the late time behavior of flows on rotating surfaces, i.e., that of the planetary flows. The simulation experiments show second order accuracy of the scheme for the structured-triangular meshes, and first order accuracy for the otherwise unstructured meshes. The method exhibits second order kinetic energy relative error convergence rate with mesh size for inviscid flows. The test case of flow on a rotating sphere demonstrates that the method preserves the stationary state, and conserves the inviscid invariants over an extended period of time.
TL;DR: In this article, a finite element method applied to a continuous downscaling data assimilation algorithm for the numerical approximation of the two-and three-dimensional Navier-Stokes equilibria is presented.
Abstract: In this paper we analyze a finite element method applied to a continuous downscaling data assimilation algorithm for the numerical approximation of the two- and three-dimensional Navier--Stokes equ...
TL;DR: It is proved the global well-posedness of the solutions, and the existence of the pullback attractor for the associated process, and a family of invariant Borel probability measures is constructed, which is supported by the pull back attractor.
TL;DR: A continuous data assimilation algorithm proposed by Azouani, Olson, and Titi (AOT) in the context of an unknown viscosity is studied and the large-time error between the true solution of t is determined.
Abstract: We study a continuous data assimilation algorithm proposed by Azouani, Olson, and Titi (AOT) in the context of an unknown viscosity. We determine the large-time error between the true solution of t...
TL;DR: In this paper, Liouville type theorems for the three dimensional steady-state Navier-Stokes equations were proved for the case where the velocity field belongs to some Lorentz space.
Abstract: Our aim is to prove Liouville type theorems for the three dimensional steady-state Navier-Stokes equations provided the velocity field belongs to some Lorentz spaces. The corresponding statement contains several known results as a particular case.
TL;DR: In this article, a review focusing on 3D Navier-Stokes equations and dyadic models of turbulence is presented, where regularization by noise for certain classes of fluid dynamic equations, a theme dear to Giuseppe Da Prato, is discussed.
Abstract: Regularization by noise for certain classes of fluid dynamic equations, a
theme dear to Giuseppe Da Prato [23], is reviewed focusing on 3D Navier-Stokes
equations and dyadic models of turbulence.
TL;DR: In this article, the authors studied axially symmetric D-solutions of the 3D Navier-Stokes equations and proved a vanishing result for the case of R 2 × I with suitable boundary conditions.
TL;DR: In this article, the authors established the energy equality for weak solutions in a large class of function spaces and showed that these conditions are weak-in-time with optimal space regularity and therefore weaker than previous classical results.
Abstract: Onsager's conjecture for the 3D Navier–Stokes equations concerns the validity of energy equality of weak solutions with regards to their smoothness. In this note, we establish the energy equality for weak solutions in a large class of function spaces. These conditions are weak-in-time with optimal space regularity and therefore weaker than previous classical results. Heuristics using intermittency argument and divergence-free counterexamples are given, indicating the possible sharpness of our conditions.
TL;DR: This work develops the first discretizations for compressible computational fluid dynamics that are primary conservative, locally entropy stable in the fully discrete sense under a usual CFL condition, explicit except for the parallelizable solution of a single scalar equation per element, and arbitrarily high-order accurate in space and time.
Abstract: Recently, relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation. Here, we generalize this approach to guarantee local entropy inequalities for finitely many convex functionals (entropies) and apply the resulting methods to the compressible Euler and Navier–Stokes equations. Based on the unstructured h p -adaptive SSDC framework of entropy conservative or dissipative semidiscretizations using summation-by-parts and simultaneous-approximation-term operators, we develop the first discretizations for compressible computational fluid dynamics that are primary conservative, locally entropy stable in the fully discrete sense under a usual CFL condition, explicit except for the parallelizable solution of a single scalar equation per element, and arbitrarily high-order accurate in space and time. We demonstrate the accuracy and the robustness of the fully-discrete explicit locally entropy-stable solver for a set of test cases of increasing complexity.
TL;DR: The main goal of this work is to propose an alternative approach, which relies on the residual based stabilization techniques customarily employed in the Finite Element literature, such as Brezzi-Pitkaranta, Franca-Hughes, streamline upwind Petrov-Galerkin, Galerkin Least Square.
Abstract: It is well known in the Reduced Basis approximation of saddle point problems that the Galerkin projection on the reduced space does not guarantee the inf–sup approximation stability even if a stable high fidelity method was used to generate snapshots. For problems in computational fluid dynamics, the lack of inf–sup stability is reflected by the inability to accurately approximate the pressure field. In this context, inf–sup stability is usually recovered through the enrichment of the velocity space with suitable supremizer functions. The main goal of this work is to propose an alternative approach, which relies on the residual based stabilization techniques customarily employed in the Finite Element literature, such as Brezzi–Pitkaranta, Franca–Hughes, streamline upwind Petrov–Galerkin, Galerkin Least Square. In the spirit of offline–online reduced basis computational splitting, two such options are proposed, namely offline-only stabilization and offline–online stabilization. These approaches are then compared to (and combined with) the state of the art supremizer enrichment approach. Numerical results are discussed, highlighting that the proposed methodology allows to obtain smaller reduced basis spaces (i.e., neglecting supremizer enrichment) for which a modified inf–sup stability is still preserved at the reduced order level.
TL;DR: In this article, the problem of energy conservation for the initial-boundary value problem associated to the 3D Navier-Stokes equations, with Dirichlet boundary conditions, was studied.
Abstract: In this paper we study the problem of energy conservation for the solutions of the initial–boundary value problem associated to the 3D Navier–Stokes equations, with Dirichlet boundary conditions. First, we consider Leray–Hopf weak solutions and we prove some new criteria, involving the gradient of the velocity. Next, we compare them with the existing literature in scaling invariant spaces and with the Onsager conjecture. Then, we consider the problem of energy conservation for very-weak solutions, proving energy equality for distributional solutions belonging to the so-called Shinbrot class. A possible explanation of the role of this classical class of solutions, which is not scaling invariant, is also given.
TL;DR: In this article, an improved Nernst-Planck-Poisson model was proposed for compressible isothermal electrolytes in non-equilibrium, and the elastic deformation of the medium, that induces an inherent coupling of mass and momentum transport, was taken into account.
Abstract: We consider an improved Nernst–Planck–Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non-equilibrium. The elastic deformation of the medium, that induces an inherent coupling of mass and momentum transport, is taken into account. The model consists of convection–diffusion–reaction equations for the constituents of the mixture, of the Navier–Stokes equation for the barycentric velocity and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, cross-diffusion phenomena must occur, and the mobility matrix (Onsager matrix) has a non-trivial kernel. In this paper, we establish the existence of a global-in-time weak solution, allowing for a general structure of the mobility tensor and for chemical reactions with fast nonlinear rates in the bulk and on the active boundary. We characterise the singular states of the system, showing that the chemical species can vanish only globally in space, and that this phenomenon must be concentrated in a compact set of measure zero in time.