Full Navier Research Articles

Stability of Non-constant Equilibrium Solutions for the Full Compressible Navier–Stokes–Maxwell System

In this article we consider a Cauchy problem for the full compressible Navier–Stokes–Maxwell system arising from viscosity plasmas. This system is quasilinear hyperbolic–parabolic. With the help of techniques of symmetrizers and the smallness of non-constant equilibrium solutions, we establish that global smooth solutions exist and converge to the equilibrium solution as the time approaches infinity. This result is obtained for initial data close to the steady-states. As a byproduct, we obtain the global stability of solutions near the equilibrium states for the full compressible Navier–Stokes–Poisson system in a three-dimensional torus.

A mechanism for the amplification of interface distortions on liquid jets

Abstract

Refined blow-up criteria for the full compressible Navier–Stokes equations involving temperature

In this paper, inspired by the study of the energy flux in local energy inequality of the 3D incompressible Navier–Stokes equations, we improve almost all the blow-up criteria involving temperature to allow the temperature in its scaling invariant space for the 3D full compressible Navier–Stokes equations. Enlightening regular criteria via pressure \(\Pi =\frac{\text{ divdiv }}{-\Delta }(u_{i}u_{j})\) of the 3D incompressible Navier–Stokes equations on bounded domain, we generalize Beirao da Veiga’s result in (Chin Ann Math Ser B 16:407–412, 1995) from the incompressible Navier–Stokes equations to the isentropic compressible Navier–Stokes system in the case away from vacuum.

Low stratification of a heat-conducting fluid in a time-dependent domain

We study the low Mach number limit of the full Navier–Stokes–Fourier system in the case of low stratification with ill-prepared initial data for the problem stated on a moving domain with a prescribed motion of the boundary. Similarly as in the case of a fixed domain, we recover as a limit the Oberback–Boussinesq system; however, we identify one additional term in the temperature equation of the limit system which is related to the motion of the domain and which is not present in the case of a fixed domain. One of the main ingredients in the proof is the properties of the Helmholtz decomposition on moving domains and the dependence of eigenvalues and eigenspaces of the Neumann Laplace operator on time.

Discrete Projections: A Step Towards Particle Methods on Bounded Domains without Remeshing

We propose a simple tweak to a recently developed regularisation scheme for particle methods. This allows us to chose the particle spacing $h$ proportional to the regularisation length $\sigma$ and achieve optimal error bounds of the form $\mathcal{O}(\sigma^n)$, $n\in\mathbb{N}$, without any need of remeshing. We prove this result for the linear advection equation but also carry out high-order experiments on the full Navier--Stokes equations. In our experiments the particle methods proved to be highly accurate, long-term stable, and competitive with discontinuous Galerkin methods.

Local classical solutions to the full compressible Navier–Stokes system with temperature-dependent heat conductivity

Local classical solutions to the full compressible Navier–Stokes system with temperature-dependent heat conductivity

Stationary solutions of outflow problem for full compressible Navier–Stokes–Poisson system: existence, stability and convergence rate

Stationary solutions of outflow problem for full compressible Navier–Stokes–Poisson system: existence, stability and convergence rate

Stability of degenerate stationary solution to the outflow problem for full Navier–Stokes equations

This paper is concerned with the large-time behavior of solutions to the outflow problem of full compressible Navier-Stokes equations in the half line. This is one of the series of papers by the authors on the stability of nonlinear waves to the outflow problem. We show the time asymptotic stability of degenerate (transonic) stationary solution for the general gas including ideal polytropic gas. The key point of the proof is based the new property of the degenerate stationary solution and the delicate energy estimates.

Uniform regularity of the compressible full Navier–Stokes–Maxwell system

In this paper, we prove the uniform regularity of the compressible full Navier–Stokes–Maxwell system in $$\mathbb {T}^3$$ .

Patching Hele-Shaw Cells to Investigate the Flow at Low Reynolds Number in Fracture Networks

This research has found a novel computationally efficient method of modelling flow at low Reynolds number through fracture networks. The numerical analysis was performed by connecting Hele-Shaw cells to investigate the effect of intersections on the pressure field and hydraulic resistance for given inlet and outlet pressure values. In this analysis, the impact of intersecting length, intersecting angle and fracture aperture on the fluid flow was studied. For this purpose, two models with different topologies were established. The Hele-Shaw simulation results for hydraulic resistance, pressure and velocity agreed well with results obtained by solving the full Navier–Stokes equations (NSE). The results indicated an approximately linear relationship between intersection length and hydraulic resistance. Specifically, an increase in the intersection length increases the flow rate and as a result, the pressure along the intersection length decreases. The error associated with employing the Hele-Shaw approximation in comparison with NSE is less than 2%. All investigations were performed in the Reynolds Number range of 1–10.

Long-time dynamics of internal wave streaming

Abstract

Restricted optimal paths to transition in a plane Couette flow

To identify laminar/turbulent transition paths in plane Couette flow, a variational formulation incorporating a restricted nonlinear (RNL) system that retains a single streamwise Fourier mode, is used. Considering the flow geometry originally used by Monokrousos et al. (2011) and Duguet et al. (2013) and the same Reynolds numbers (Re), we show that initial perturbations obtained by RNL optimizations exhibit spatial localization. Two optimal states are found with comparable initial energy levels above which the flow structure evolves to turbulence. It is found that this level is twice that of the minimal threshold energy which has been obtained using the full nonlinear equations (Duguet et al. (2013)). Especially, the Re dependence of energy thresholds is studied within a RNL optimization framework for the first time, with evidence for a ORe−2.65 scaling close to the one found using the full Navier–Stokes equations (ORe−2.7). The first state is obtained for a short target time. It is symmetric with respect to the mid-plane y=0 and spanwise localized. For a long target time, the optimal appears to be localized in both spanwise and wall-normal directions. The mechanisms highlighted within the scope of nonlinear nonmodal theory (Kerswell (2018)): Orr mechanism, oblique wave interaction, lift-up, streak breakdown, localized pocket of turbulence and turbulence spreading, are also observed in the RNL simulations. Although greatly simplified, the RNL system provides a good approximation of these different fundamental mechanisms. The analysis gives then some insight into the potential of RNL optimizations for estimating Re scaling laws and routes to turbulence for shear flows.

On the Calculation of Propulsive Characteristics of a Bulk-Carrier Moving in Head Seas

The present work describes a simplified Computational Fluid Dynamics (CFD) approach in order to calculate the propulsive performance of a ship moving at steady forward speed in head seas. The proposed method combines experimental data concerning the added resistance at model scale with full scale Reynolds Averages Navier–Stokes (RANS) computations, using an in-house solver. In order to simulate the propeller performance, the actuator disk concept is employed. The propeller thrust is calculated in the time domain, assuming that the total resistance of the ship is the sum of the still water resistance and the added component derived by the towing tank data. The unsteady RANS equations are solved until self-propulsion is achieved at a given time step. Then, the computed values of both the flow rate through the propeller and the thrust are stored and, after the end of the examined time period, they are processed for calculating the variation of Shaft Horsepower (SHP) and RPM of the ship’s engine. The method is applied for a bulk carrier which has been tested in model scale at the towing tank of the Laboratory for Ship and Marine Hydrodynamics (LSMH) of the National Technical University of Athens (NTUA).

Global well-posedness to the 3D Cauchy problem of compressible non-isothermal nematic liquid crystal flows with vacuum

We are concerned with global well-posedness of strong solutions to the Cauchy problem for compressible non-isothermal nematic liquid crystal flows with vacuum as far field density in R3. By using energy method, we establish the global existence and uniqueness of strong solutions provided that the quantity‖ρ0‖L∞+‖∇d0‖L3 is suitably small and the viscosity coefficients verify 3μ>λ. In particular, the initial density can even have compact support. When d is a constant vector and |d|=1, we also extend partially the corresponding result in Li (2020) where the global small solution of full compressible Navier–Stokes equations was obtained under the condition 2μ>λ. To our knowledge, the result in this paper could be viewed as the first one on the global existence of strong solutions to 3D Cauchy problem for compressible non-isothermal nematic liquid crystal flows with vacuum.

Modelling of Thin CNTs Nanoliquid Film Flow Over a Bi-directional Stretching Surface

Unsteady flow of water and ethylene-glycol based carbon nanotubes (CNTs) nanoliquid film is examined on a bi-directional stretching surface under influence of transverse magnetic field and thermal radiation. Single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) are considered within the base liquid for investigation. Guiding full Navier–Stokes and energy equations were simplified using the thin film approximations and solved using the method of the asymptotic expansion. The result shows that nanoliquid thinning rate diminishes with rising values of CNTs volume fraction, Hartmann number and Biot number. The result also indicates that the thinning rate is more for MWCNTs with reference to the SWCNTs. It is seen that film thinning rate enhances for water-MWCNTs nanoliquid but reverse scenario is found for ethylene-glycol MWCNTs nanoliquid. The effect of various physical parameters on temperature profile has been discussed.

Robust aerodynamic shape optimization using a novel multi-objective evolutionary algorithm coupled with surrogate model

The fruit fly optimization algorithm (FOA) is a newly developed bio-inspired algorithm that has exhibited enormous values in engineering optimization. In this study, an effective multi-objective fruit fly optimization algorithm (MOFOA) incorporated with the Pareto dominance is investigated and applied to robust aerodynamic shape optimization considering uncertainties in the design process. In the MOFOA, the fruit flies are required to perform solution explorations within an adaptive search scope by flying around the Pareto non-dominated solutions. An enhanced clustering evolution mechanism of combining the cooperative local search and differential evolution operator is elaborately designed to enrich the exploratory capacities for complex optimization. Paired with the search strategy, the non-dominated sorting technique considering the quality as well as uniform distribution of Pareto solutions is adopted to deal with the multiple objectives. To generate high-quality and uniformly spread-out Pareto non-dominated solutions, the roulette wheel selection (RWS) operator based on crowding distance is employed to guide the selection processes of individuals throughout various stages of the MOFOA. The effectiveness and superiority of MOFOA are demonstrated by the comparative studies on several benchmark functions. Finally, a robust aerodynamic design system for combining the MOFOA optimizer with a Kriging-based surrogate model and full Navier–Stokes computation is advantageously implemented to perform shape optimization on a transonic airfoil using the Taguchi robust design methodology that emphasizes the inherent variability while improving engineering productivity. The design results show that the robust design, compared with the single-point design, is capable of producing a set of robust solutions that are significantly less sensitive to input variations by capturing the Pareto-optimal front with respect to the criteria of aerodynamic performance and its stability.

Resonance phenomena in a channel with oscillating walls

In the article we consider the flow of viscous compressible fluid in a channel with oscillating walls. The obtained solutions of linearized Navier–Stokes equations suggest that resonance phenomena are possible under certain conditions, namely, under the particular relation between the frequency of wall vibration, the geometrical characteristics of a channel and speed of sound in the fluid. Resonance phenomena result in the periodical changes of flow parameters with maximum amplitude. The numerical simulations based on full Navier–Stokes equations show that great increase in the mass rate of the flow can occur even if fluid is pumped at constant pressure gradient.

Variational multiscale modeling with discretely divergence-free subscales

We introduce a residual-based stabilized formulation for incompressible Navier–Stokes flow that maintains discrete (and, for divergence-conforming methods, strong) mass conservation for inf–sup stable spaces with H1-conforming pressure approximation, while providing optimal convergence in the diffusive regime, robustness in the advective regime, and energetic stability. The method is formally derived using the variational multiscale (VMS) concept, but with a discrete fine-scale pressure field which is solved for alongside the coarse-scale unknowns such that the coarse and fine scale velocities separately satisfy discrete mass conservation. We show energetic stability for the full Navier–Stokes problem, and we prove convergence and robustness for a linearized model (Oseen flow), under the assumption of a divergence-conforming discretization. Numerical results indicate that all properties extend to the fully nonlinear case and that the proposed formulation can serve to model unresolved turbulence.

Development of a stagnation streamline model for thermochemical nonequilibrium flow

A stagnation streamline model incorporating quantum-state-resolved chemistry is proposed to study hypersonic nonequilibrium flows along the stagnation streamline. This model is developed by reducing the full Navier–Stokes equations to the stagnation streamline with proper approximations for equation closure. The thermochemical nonequilibrium is described by either the state-to-state approach for detailed analysis or conventional two-temperature models for comparison purpose. The model is validated against various data, and nearly identical results are obtained as compared with those from full field computational fluid dynamics data. In addition, the calculated distributions agree well with the measurement data of a shock tube experiment for the dissociation and vibrational relaxation of O2, including the distributions of species mole fractions and vibrational temperature of the first excited state of O2 molecules. Furthermore, the results with the state-resolved chemistry show that the flow within a shock layer exhibits a strong thermochemical nonequilibrium behavior, which is beyond the capability of commonly used two-temperature models to correctly evaluate the dissociation rate and the associated reaction energy. The present model is also employed to calculate the nonequilibrium re-entry flow along the stagnation streamline for a five-species air mixture as an example to demonstrate the model capability. It is found that both species and internal energy are in a nonequilibrium state, especially the vibrational distributions are strongly deviated from the Boltzmann distribution right behind the bow shock and near the wall surface. The results demonstrate that the proposed stagnation streamline model is very useful to understand thermochemical nonequilibrium phenomena in hypersonic flows.

Global well-posedness of non-heat conductive compressible Navier–Stokes equations in 1D

In this paper, the initial-boundary value problem of the one-dimensional full compressible Navier–Stokes equations with positive constant viscosity but with zero heat conductivity is considered. Global well-posedness is established for any H1 initial data. The initial density is assumed only to be nonnegative, and, thus, is not necessary to be uniformly away from vacuum. Comparing with the well-known result of Kazhikhov and Shelukhin (1977 J. Appl. Math. Mech. 41 273–282), the heat conductive coefficient is zero in this paper, and the initial vacuum is allowed.