Solution Of Navier Research Articles

Numerical Modelling of Static Aeroelastic Deformations of Slender Wing in Aerodynamic Design

Abstract The article presents the validation of two methods for analyzing the aerodynamic properties of the aircraft wing concerning aeroelastic effects. The first method is based on low-cost computational models (Euler–Bernoulli Beam Model and Vortex Lattice Method [VLM]). Its primary objective is to estimate the wing’s deformation early in the design stages and during the automatic optimization process. The second one is a method that uses solutions of unsteady Navier–Stokes equations (URANS). This method suits early design, particularly for unconventional designs or flight conditions exceeding lowfidelity method limits. The coupling of the flow and structural models was done by Radial Basis Functions implemented as a user-defined module in the ANSYS Fluent solver. The structural model has variants for linear and nonlinear wing deformations. Features enhancing applicability for real-life applications, such as the definition of deformable and nondeformable mesh zones with smooth transition between them, have been included in this method. A rectangular wing of a high-altitude long-endurance (HALE) aeroplane, built based on the NACA 0012 profile, was used to validate both methods. The resulting deflections and twists of the wing have been compared with reference data for the linear and nonlinear variants of the model.

Numerical Analysis of Rarefied Gas Flow through a System of Short Channels

The S-model kinetic equation is used to study the rarefied gas flow from a high-pressure tank to a low-pressure one through a flat membrane with a finite number of pores. The kinetic equation is solved numerically using a second-order accurate implicit conservative method implemented in the in-house code Nesvetay. For transitional and continuum flow regimes, numerical solutions of the compressible Navier–Stokes equations are obtained. The gas flow rate through the system of pores and the forces acting on the membrane bars are investigated as functions of the Knudsen number (Kn) at a pressure ratio of 2 : 1 in the tanks. The features of the flow field near the membrane and away from it are described.

Three-dimensional laminar flow using physics informed deep neural networks

Physics informed neural networks (PINNs) have demonstrated their effectiveness in solving partial differential equations (PDEs). By incorporating the governing equations and boundary conditions directly into the neural network architecture with the help of automatic differentiation, PINNs can approximate the solution of a system of PDEs with good accuracy. Here, an application of PINNs in solving three-dimensional (3D) Navier–Stokes equations for laminar, steady, and incompressible flow is presented. Notably, our approach involves deploying PINNs using feed-forward deep neural networks (DNNs) without depending on any simulation or experimental data. This investigation focuses on 3D square channel flow and 3D lid-driven cavity flow. For each case, one deep neural network was trained using only the governing equations and boundary conditions. Finally, the PINNs' results were compared with the computational fluid dynamics results. The goal was to assess the ability of PINNs (with DNN architectures) to predict the solution of Navier–Stokes equations in the 3D domain without any simulation or experimental data (unsupervised learning).

Global symmetric solutions of compressible Navier–Stokes equations for a reacting mixture in unbounded domains

Global symmetric solutions of compressible Navier–Stokes equations for a reacting mixture in unbounded domains

Uniform approximation of 2D Navier-Stokes equations with vorticity creation by stochastic interacting particle systems

We consider a stochastic interacting particle system in a bounded domain with reflecting boundary, including creation of new particles on the boundary prescribed by a given source term. We show that such particle system approximates 2D Navier–Stokes equations in vorticity form and impermeable boundary, the creation of particles modeling vorticity creation at the boundary. Kernel smoothing, more specifically smoothing by means of the Neumann heat semigroup on the space domain, allows to establish uniform convergence of regularized empirical measures to (weak solutions of) Navier–Stokes equations.

Application of computationally inexpensive CFD model in steady-state and transient simulations of pulverized sewage sludge combustion

The combustion process of pulverized fuels with high ash contents, such as sewage sludge, is significantly impacted by the amount of slag deposition in a furnace. A CFD model based on the Steady Diffusion Flamelet (SFM) approach was applied to numerically simulate the combustion of pulverized sewage sludge in a drop tube furnace. Steady-state solutions of the Reynolds-Averaged Navier–Stokes (RANS) equations already displayed good agreement with species and temperature measurements. Still, they failed to accurately predict the significant amount of ash trapped on the internal furnace surfaces (minimum deposition of 28% of the generated ash versus 5% predicted by the RANS simulations). The SFM-based CFD model’s computational efficiency enabled the conduction of large eddy simulations (LES), significantly improving the model’s predictive capabilities (27% of the generated ash deposited). Additionally, the transient simulations further improved the agreement with temperature measurement data. A novel initialization procedure was developed, which allowed the transient LES simulations to be conducted in a computationally efficient manner. The SFM-based model can effectively support research and development efforts, even for large-scale systems which require high cell counts. It provides valuable insights during the early design phases of industrial furnaces for pulverized sewage sludge combustion.

Three-dimensional stochastic Navier–Stokes equations with Markov switching

A finite-state Markov chain is introduced in the noise terms of the three-dimensional stochastic Navier–Stokes equations in order to allow for transitions between two types of multiplicative noises. We call such systems as stochastic Navier–Stokes equations with Markov switching. To solve such a system, a family of regularized stochastic systems is introduced. For each such regularized system, the existence of a unique strong solution (in the sense of stochastic analysis) is established by the method of martingale problems and pathwise uniqueness. The regularization is removed in the limit by obtaining a weakly convergent sequence from the family of regularized solutions, and identifying the limit as a solution of the three-dimensional stochastic Navier–Stokes equation with Markov switching.

On the Stability of Periodic Solutions of a Model Navier–Stokes Equation in a Thin Layer

On the Stability of Periodic Solutions of a Model Navier–Stokes Equation in a Thin Layer

Global existence and non-uniqueness for the Cauchy problem associated to 3D Navier–Stokes equations perturbed by transport noise

We show global existence and non-uniqueness of probabilistically strong, analytically weak solutions of the three-dimensional Navier–Stokes equations perturbed by Stratonovich transport noise. We can prescribe either: (i) any divergence-free, square integrable intial condition; or (ii) the kinetic energy of solutions up to a stopping time, which can be chosen arbitrarily large with high probability. Solutions enjoy some Sobolev regularity in space but are not Leray–Hopf.

The Navier–Stokes equations with body forces decaying coherently in time

The long-time behavior of solutions of the three-dimensional Navier–Stokes equations in a periodic domain is studied. The time-dependent body force decays, as time t tends to infinity, in a coherent manner. In fact, it is assumed to have a general and complicated asymptotic expansion which involves complex powers of et, t, ln⁡t, or other iterated logarithmic functions of t. We prove that all Leray–Hopf weak solutions admit an asymptotic expansion which is independent of the solutions and is uniquely determined by the asymptotic expansion of the body force. The proof makes use of the complexifications of the Gevrey–Sobolev spaces together with those of the Stokes operator and the bilinear form of the Navier–Stokes equations.

A short remark on inviscid limit of the stochastic Navier–Stokes equations

In this article, we study the inviscid limit of the stochastic incompressible Navier–Stokes equations in three-dimensional space. We prove that a subsequence of weak martingale solutions of the stochastic incompressible Navier–Stokes equations converges strongly to a weak martingale solution of the stochastic incompressible Euler equations in the periodic domain under the well-accepted hypothesis, namely Kolmogorov hypothesis (K41).

A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations

In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner. We first derive continuous energy estimates, and then proceed to the discrete setting. We formulate the discrete approximation using high-order finite difference methods on summation-by-parts form and implement the boundary conditions weakly using the simultaneous approximation term method. By applying the discrete energy method and imitating the continuous analysis, the discrete estimate that resembles the continuous counterpart is obtained proving stability. We also show that these newly derived boundary conditions removes the singularities associated with the null-space of the nonlinear discrete spatial operator. Numerical experiments that verifies the high-order accuracy of the scheme and coincides with the theoretical results are presented. The numerical results are compared with the well-known Blasius similarity solution as well as that resulting from the solution of the incompressible Navier–Stokes equations.

Well-Posedness of Mild Solutions for the Fractional Navier–Stokes Equations in Besov Spaces

Well-Posedness of Mild Solutions for the Fractional Navier–Stokes Equations in Besov Spaces

Data-physics driven multiscale approach for high-pressure resin transfer molding (HP-RTM)

We present a multiscale computational framework for high-pressure resin transfer molding of fiber-reinforced composites. Due to the relatively rapid speed of resin flow and the significant convective effects, this process is governed by the nonlinear steady-state Navier–Stokes equations, as opposed to the linear Stokes equations commonly adopted for the simulation of classical resin transfer molding processes. To overcome the computational challenge of directly solving the high-pressure resin filling problem through the fiber preform, we developed a data-driven nonlinear homogenization approach where the average velocity and instantaneous permeability computed from the microscale representative volume element problem provide solution-dependent coefficients for the macroscale problem. The proposed data-physics driven computational framework has been validated against the direct numerical solution of the steady-state Navier–Stokes equations.

A physics-based reduced order model for urban air pollution prediction

This article presents an innovative approach for developing an efficient reduced-order model to study the dispersion of urban air pollutants. The need for real-time air quality monitoring has become increasingly important, given the rise in pollutant emissions due to urbanization and its adverse effects on human health. The proposed methodology involves solving the linear advection–diffusion problem, where the solution of the Reynolds-averaged Navier–Stokes (RANS) equations gives the convective field. At the same time, the source term consists of an empirical time series.However, the computational requirements of this approach, including microscale spatial resolution, repeated evaluation, and low time scale, necessitate the use of high-performance computing facilities, which can be a bottleneck for real-time monitoring. To address this challenge, a problem-specific methodology was developed that leverages a data-driven approach based on Proper Orthogonal Decomposition with regression (POD-R) coupled with Galerkin projection (POD-G) endorsed with the discrete empirical interpolation method (DEIM). The proposed method employs a feedforward Neural Network (NN) to non-intrusively retrieve the reduced-order convective operator required for online evaluation. The numerical framework was validated on synthetic emissions and real wind measurements.The results demonstrate that the proposed approach significantly reduces the computational burden of the traditional approach and is suitable for real-time air quality monitoring. Overall, the study advances the field of reduced order modeling and highlights the potential of data-driven approaches in environmental modeling and large-scale simulations.

A surface finite element method for the Navier–Stokes equations on evolving surfaces

AbstractWe introduce a surface finite element method for the numerical solution of Navier–Stokes equations on evolving surfaces with a prescribed deformation of the surface in the normal direction. The method is based on approaches for the full surface Navier–Stokes equations in the context of fluid‐deformable surfaces and adds a penalization of the normal component of the velocity. Numerical results demonstrate the same optimal order of convergence as proposed for surface (Navier–)Stokes equations on stationary surfaces. The approach is applied to high‐resolution three‐dimensional scans of clothed bodies in motion to provide interactive virtual fluid‐like clothing.

Global strong solutions of 3D compressible Navier–Stokes equations with short pulse type initial data

Global strong solutions of 3D compressible Navier–Stokes equations with short pulse type initial data

Energy equality for weak solutions of the compressible Navier–Stokes–Korteweg equations with general pressure law in a bounded domain

In this paper, we study the energy equality for weak solutions to the compressible Navier–Stokes–Korteweg equations with general pressure law in a bounded domain Ω⊂Rd (d=2,3). By exploring the special structure of the nonlinear terms, and using coarea formula, we formulate the sufficient conditions for the regularity of weak solutions to ensure that energy equality holds.

Evaluation of temperature and concentration fields from refractive index field for evaporation-induced convective flow

The present work relates to the simultaneous determination of concentration and temperature fields from a refractive index field, and is motivated by applications in evaporation. Several optical measurement techniques such as schlieren and interferometry can measure the refractive index field, which can then be converted to a density and temperature field for a single component system. The refractive index, however, is dependent on both temperature and concentration for a multi-component system involving combined heat and mass transfer. Hence, either the temperature or concentration field must be known to obtain the other. To circumvent this issue, several methods are evaluated in this study to extract concentration and temperature fields from a refractive index field. The evaluation is performed based on data from a coupled numerical solution of Navier–Stokes, energy and species conservation equations. The refractive index field can be obtained from this computed temperature and concentration field. This refractive index field is then separately used to obtain the combined temperature-concentration field using the method proposed in this work. This method is based on the premise that there is a relationship between temperature and concentration fields which can help to independently calculate both when the refractive index field is known. The temperature and concentration fields obtained using this approach are then compared with the originally computed field and the errors in them are estimated for a wide range of Lewis numbers. From the study, it is concluded that the proposed methods can be used to accurately determine the temperature and concentration fields from a given refractive index field.

Global smooth solution of compressible Navier–Stokes system with temperature-dependent transport coefficients and pressure condition

Global smooth solution of compressible Navier–Stokes system with temperature-dependent transport coefficients and pressure condition