Compressible Viscous Fluid Research Articles

Numerical simulation of a complex moving rigid body under the impingement of a shock wave in 3D

In this paper, we take a numerical simulation of a complex moving rigid body under the impingement of a shock wave in three-dimensional space. Both compressible inviscid fluid and viscous fluid are considered with suitable boundary conditions. We develop a high order numerical boundary treatment for the complex moving geometries based on finite difference methods on fixed Cartesian meshes. The method is an extension of the inverse Lax-Wendroff (ILW) procedure in our works (Cheng et al., Appl Math Mech (Engl Ed) 42: 841–854, 2021; Liu et al.) for 2D problems. Different from the 2D case, the local coordinate rotation in 3D required in the ILW procedure is not unique. We give a theoretical analysis to show that the boundary treatment is independent of the choice of the rotation, ensuring the method is feasible and valid. Both translation and rotation of the body are taken into account in this paper. In particular, we reformulate the material derivative for inviscid fluid on the moving boundary with no-penetration condition, which plays a key role in the proposed algorithm. Numerical simulations on the cylinder and sphere are given, demonstrating the good performance of our numerical boundary treatments.

Global existence of weak solutions to the Navier–Stokes–Korteweg equations

In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove global existence of finite energy weak solutions for large initial data. Contrary to previous results regarding this system, vacuum regions are allowed in the definition of weak solutions and no additional damping terms are considered. The convergence of the approximating solutions is obtained by introducing suitable truncations in the momentum equations of the velocity field and the mass density at different scales and use only the a priori bounds obtained by the energy and the BD entropy. Moreover, the approximating solutions enjoy only a limited amount of regularity, and the derivation of the truncations of the velocity and the density is performed by a suitable regularization procedure.

Direct Numerical Simulation of Fully Developed Turbulent Gas–Particle Flow in a Duct

Direct numerical simulation of a fully developed turbulent flow of a viscous compressible fluid containing spherical solid particles in a channel is carried out. The formation of regions with an increased concentration of solid particles in a fully developed turbulent flow in a channel with solid walls is considered. The fluid flow is simulated with unsteady three-dimensional Navier – Stokes equations. The discrete trajectory approach is applied to simulate the motion of particles. The distributions of the mean and fluctuating characteristics of the fluid flow and distribution of the concentration of the dispersed phase in the channel are discussed. The formation of regions with an increased concentration of particles is associated with the instantaneous distribution of vorticity in the near-wall region of the channel. The results of numerical simulation are in qualitative and quantitative agreement with the available data of physical and computational experiments.

Numerical simulation of the gas flow with radiation and heat transfer

In this article we focus on the heating of the solid body placed in the vicinity of the intense heat source. We simulate the heat transfer caused by the direct contact with surrounding heated gas. Furthermore it is necessary to take into account the heat transfer caused by the radiation, which radically affects the resulting heat flux. We work with the non-stationary viscous compressible fluid flow with additional heat sources, described by the RANS equations. The heat radiation is simulated using other supplemented equations. The heat transfer equations are solved inside the considered body.

Two phase flows of compressible viscous fluids

<p style='text-indent:20px;'>We introduce a new concept of <i>dissipative varifold solution</i> to models of two phase compressible viscous fluids. In contrast with the existing approach based on the Young measure description, the new formulation is variational combining the energy and momentum balance in a single inequality. We show the existence of dissipative varifold solutions for a large class of general viscous fluids with non–linear dependence of the viscous stress on the symmetric velocity gradient.</p>

Simulation of Counter-Current Spontaneous Imbibition Based on Momentum Equations with Viscous Coupling, Brinkman Terms and Compressible Fluids

A numerical model is investigated representing counter-current spontaneous imbibition of water to displace oil or gas from a core plug. The model is based on mass and momentum conservation equations in the framework of the theory of mixtures. We extend a previous imbibition model that included fluid–rock friction and fluid–fluid drag interaction (viscous coupling) by including fluid compressibility and Brinkman viscous terms. Gas compressibility accelerated recovery due to gas expansion from high initial non-wetting pressure to ambient pressure at typical lab conditions. Gas compressibility gave a recovery profile with two characteristic linear sections against square root of time which could match tight rock literature experiments. Brinkman terms decelerated recovery and delayed onset of imbibition. Experiments where this was prominent were successfully matched. Both compressibility and Brinkman terms caused recovery deviation from classical linearity with the square root of time. Scaling yielded dimensionless numbers when Brinkman term effects were significant.Article HighlightsSpontaneous imbibition with viscous coupling, compressibility and Brinkman terms.Viscous coupling reduces spontaneous imbibition rate by fluid–fluid friction.Brinkman terms delay early recovery and explain seen delayed onset of imbibition.Gas compressibility accelerates recovery and can be significant at lab conditions.Gas compressibility gives recovery with two root of time lines as seen for shale.

Stationary Flows for Compressible Viscous Fluid in a Perturbed Half-Space

We consider the compressible Navier--Stokes equation in a perturbed half-space with an outflow boundary condition as well as the supersonic condition. For a half-space, it has been known that a certain planar stationary solution exist and it is time-asymptotically stable. The planar stationary solution is independent of the tangential directions and its velocities of the tangential directions are zero. In this paper, we show the unique existence of stationary solutions for the perturbed half-space. The feature of our work is that our stationary solution depends on all directions and has multidirectional flow. Furthermore, we also prove the asymptotic stability of this stationary solution.

Linear stability analysis of the homogeneous Couette flow in a 2D isentropic compressible fluid

In this paper, we study the linear stability properties of perturbations around the homogeneous Couette flow for a 2D isentropic compressible fluid in the domain mathbb {T}times mathbb {R}. In the inviscid case there is a generic Lyapunov type instability for the density and the irrotational component of the velocity field. More precisely, we prove that their L^2 norm grows as t^{1/2} and this confirms previous observations in the physics literature. On the contrary, the solenoidal component of the velocity field experiences inviscid damping, namely it decays to zero even in the absence of viscosity. For a viscous compressible fluid, we show that the perturbations may have a transient growth of order nu ^{-1/6} (with nu ^{-1} being proportional to the Reynolds number) on a time-scale nu ^{-1/3}, after which it decays exponentially fast. This phenomenon is also called enhanced dissipation and our result appears to be the first to detect this mechanism for a compressible flow, where an exponential decay for the density is not a priori trivial given the absence of dissipation in the continuity equation.

The Lp energy methods and decay for the compressible Navier-Stokes equations with capillarity

We consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effect. Referring to those studies in the non-capillary case, the purpose of this paper is to investigate the dissipation effect of Korteweg tensor with the density-dependent capillarity κ(ϱ). It is observed by the pointwise estimate that the linear third-order capillarity behaves like the heat diffusion of density fluctuation, which allows to develop the Lp energy methods (independent of spectral analysis). As a result, the time-decay estimates of Lq-Lr type regarding this system can be established. The treatment of nonlinear capillarity depends mainly on new Besov product estimates and the elaborate use of Sobolev embeddings and interpolations. Our results can be also applied to the quantum Navier-Stokes system, since it is a special choice of capillarity κ(ϱ)=κ/ϱ.

Weak–strong uniqueness property for models of compressible viscous fluids near vacuum* *The work of EF was supported by the Czech Sciences Foundation (GAČR), Grant Agreement 21-02411S. The work of AN was partially supported by the Eduard Čech visiting program at the Mathematical Institute of the Academy of Sciences of the Czech Republic.

We extend the weak–strong uniqueness principle to general models of compressible viscous fluids near/on the vacuum. In particular, the physically relevant case of positive density with polynomial decay at infinity is considered.

On stationary convective motion of viscous compressible and heat-conductive fluid

We consider in an infinite horizontal layer the stationary convective flow of a viscous compressible and heat-conductive fluid subject to gravitational force, where the slip boundary condition for the velocity and the boundary condition of the temperature near the hydrostatic distribution are assumed. The existence of stationary solution close to hydrostatic state is obtained in Sobolev spaces as limit of fixed points of some suitable operators.

Predictive control of Si content in blast furnace smelting based on improved SA-BP

Blast furnace smelting process is a highly complex nonlinear dynamic process, its purpose is to refining the quality of liquid iron. From the point of view of chemical reaction kinetics, the main chemical reactions in the blast furnace are as many as 108 kinds, and the high complexity is obvious. From the point of view of hydrodynamics, there are three-phase mixed compressible viscous fluids in the blast furnace smelting process. The hydrodynamic equation is nonlinear, high-dimensional and high-coupling. In addition, the blast furnace smelting process has the characteristics of time-varying, high-dimensional, distributed parameters and other characteristics of the complex conditions and the failure of the operation under the conditions of the test, making the blast furnace smelting process automation and furnace temperature precision control to become metallurgical workers face the problem. In this study, from the data point of view, to explore the furnace temperature can be characterized by [Si] content prediction. Based on the data of 1000 furnace blast furnace, an accurate and reasonable prediction model of Si content in blast furnace is established. First of all, through the calculation of correlation coefficients of various factors and the time trend diagram, the general lag time between each parameter and Si content in the process of blast furnace production is obtained. Through correlation and analysis of the correlation between lag time, before and after the two largest furnace, with improved simulated annealing algorithm to determine the optimal initial weights, the content of Si, the N furnace of S content, the quantity of coal and air PML FL as input, the contents of Si in n+1 furnace as output to establish dynamic prediction model of improved SA-BP neural network based. Finally, the data used to detect the model is brought into the model to be tested, the error is analyzed, and the error local map is used to express the error visually. The model is tested.

Digital rock physics applied to squirt flow

We have developed a workflow for computing the seismic-wave moduli dispersion and attenuation due to squirt flow in a numerical model derived from a micro X-ray computed tomography image of cracked (through thermal treatment) Carrara marble sample. To generate the numerical model, the image is processed, segmented, and meshed. The finite-element method is adopted to solve the linearized, quasistatic Navier-Stokes equations describing laminar flow of a compressible viscous fluid inside the cracks coupled with the quasistatic Lamé-Navier equations for the solid phase. We compute the effective P- and S-wave moduli in the three Cartesian directions for a model in dry conditions (saturated with air) and for a smaller model fully saturated with glycerin and having either drained or undrained boundary conditions. For the model saturated with glycerin, the results indicate significant and frequency-dependent P- and S-wave attenuation and the corresponding dispersion caused by squirt flow. Squirt flow occurs in response to fluid pressure gradients induced in the cracks by the imposed deformations. Our digital rock-physics workflow can be used to interpret laboratory measurements of attenuation using images of the rock sample.

Compressible viscous heat-conducting surface wave without surface tension

In this paper, we consider a three-dimensional compressible viscous heat-conducting fluid in a horizontally periodic domain, bounded above by a free surface and below by a rigid bottom. The motion of the fluid is governed by the full compressible, gravity-driven Navier–Stokes equations with appropriate boundary conditions. On the free surface, the effect of surface tension is neglected, and the temperature is assumed to satisfy the Robin boundary condition. Motivated by Y. Guo and I. Tice [Anal. PDE 6, 287–369 (2013), Arch. Ration. Mech. Anal. 207, 459–531 (2013), and Anal. PDE 6, 1429–1533 (2013)], we establish the global well-posedness of this free boundary problem, provided that the initial data are close to a nontrivial equilibrium state.

On the Motion of a Compressible Viscous Fluid Driven by Time Periodic Inflow/Outflow Boundary Conditions

We consider the barotropic Navier–Stokes system describing the motion of a compressible viscous fluid confined to a bounded domain driven by time periodic inflow/outflow boundary conditions. We show that the problem admits a time periodic solution in the class of weak solutions satisfying the energy inequality.

𝐿_{𝑝}-estimates of solution of the free boundary problem for viscous compressible and incompressible fluids in the linear approximation

The paper contains L p L_p -estimates and a theorem on the local in time solvability of the problem arising as a result of linearization of the free boundary problem for two viscous fluids, compressible and incompressible, contained in a bounded vessel, separated by a free interface, and subject to mass and capillary forces. This result is known for the case of p = 2 p=2 ; it serves as an analytical basis for the study of the complete nonlinear problem. The proof is based on the “maximal regularity” estimate of the solution obtained with the help of the L p L_p Fourier multiplier theorem due to P. I. Lizorkin.

On the Long-Time Behavior of Dissipative Solutions to Models of Non-Newtonian Compressible Fluids

We identify a class maximal dissipative solutions to models of compressible viscous fluids that maximize the energy dissipation rate. Then we show that any maximal dissipative solution approaches an equilibrium state for large times.

Dissipative spatial discretization of a phase field model of multiphase multicomponent isothermal fluid flow

This work is devoted to the development of a dissipative spatial discretization of a phase field model describing the dynamics of a multicomponent multiphase isothermal viscous compressible fluid with a resolved interface and effects associated with it (surface tension, wetting). Mass densities of mixture components are used as order parameters. The total Helmholtz free energy incorporates wall free energy providing wetting effects. The model under consideration is preliminary regularized, which allows one to increase time step in explicit time-marching methods. A finite-difference semi-discrete method is proposed and a discrete counterpart of the dissipativity theorem is proven. All the statements remain valid in the absence of regularization as well. 3D simulations of two-phase two-component and three-phase three-component fluids using explicit Euler method are performed. The simulation results confirm theoretical predictions.

Global unique solvability of an initial-boundary value problem for the one-dimensional barotropic equations of binary mixtures of viscous compressible fluids

Global unique solvability of an initial-boundary value problem for the one-dimensional barotropic equations of binary mixtures of viscous compressible fluids

On the Evolution of Compressible and Incompressible Viscous Fluids with a Sharp Interface

In this paper, we consider some two phase problems of compressible and incompressible viscous fluids’ flow without surface tension under the assumption that the initial domain is a uniform Wq2−1/q domain in RN (N≥2). We prove the local in the time unique existence theorem for our problem in the Lp in time and Lq in space framework with 2<p<∞ and N<q<∞ under our assumption. In our proof, we first transform an unknown time-dependent domain into the initial domain by using the Lagrangian transformation. Secondly, we solve the problem by the contraction mapping theorem with the maximal Lp-Lq regularity of the generalized Stokes operator for the compressible and incompressible viscous fluids’ flow with the free boundary condition. The key step of our proof is to prove the existence of an R-bounded solution operator to resolve the corresponding linearized problem. The Weis operator-valued Fourier multiplier theorem with R-boundedness implies the generation of a continuous analytic semigroup and the maximal Lp-Lq regularity theorem.