Narrow Results

We consider the non-stationary 3-D flow of a compressible viscous and heat-conducting micropolar fluid with the assumption of spherical symmetry. We analyze the flow between two concentric spheres that present solid thermo-insulated walls. The fluid is perfect and polytropic in the thermodynamical sense and the initial density and temperature are strictly positive. The corresponding problem has homogeneous boundary data.

In this work, we present the described model and provide a brief overview of the progress in the mathematical analysis of the associated initial-boundary problem. We consider existence and uniqueness of the generalized solution, asymptotic behavior of the solution and regularity of the solution.

We present a particle method for the simulation of three dimensional compressible hydrodynamics based on a hybrid Particle-Mesh discretization of the governing equations. The method is rooted on the regularization of particle locations as in remeshed Smoothed Particle Hydrodynamics (rSPH).

The rSPH method was recently introduced to remedy problems associated with the distortion of computational elements in SPH, by periodically re-initializing the particle positions and by using high order interpolation kernels.

In the PMH formulation, the particles solely handle the convective part of the compressible Euler equations. The particle quantities are then interpolated onto a mesh, where the pressure terms are computed. PMH, like SPH, is free of the convection CFL condition while at the same time it is more efficient as derivatives are computed on a mesh rather than particle-particle interactions. PMH does not detract from the adaptive character of SPH and allows for control of its accuracy. We present simulations of a benchmark astrophysics problem demonstrating the capabilities of this approach.

Among the existing lattice Boltzmann models (LBMs) for compressible flow, the one by Kataoka and Tsutahara [KT model, Phys. Rev. E69, 056702 (2004)] has a simple and rigorous theoretical background. The drawback of this KT model is that it can cause numerical instability if the local Mach number exceeds 1. The precise mechanism of this instability has not yet been clarified. In this paper, we derive entropy functions whose local equilibria are suitable to recover the Euler-like equations in the framework of the lattice Boltzmann method for the KT model. Numerical examples are also given, which are consistent with the above theoretical arguments, and show that the entropy condition is not fully guaranteed in KT model. The negative entropy may be the inherent cause for the nonphysical oscillations in the vicinity of the shock. In contrast to these Karlin's microscopic entropy approach, the corresponding subsidiary entropy condition in the LBM calculation could also be deduced explicitly from the macroscopic version, which provides some insights on the numerical instability of the LBM for shock calculation.

In this paper, a high-order hybrid method for solving compressible two-phase fluid flow, including cavitation, is presented. In this regard, assuming pressure and temperature equilibrium, mass and heat transfer between the different phases are modeled. In this work, the CRMWENOZ method, which is a new combination of compact and weighted essentially non-oscillatory (WENO) methods and is more accurate than conventional methods, is presented. The new high-order hybrid method aims to predict the density and the pressure discontinuities in two-phase flow by combining the CRMWENOZ high-order method and an adaptive moving mesh technique. For this purpose, the adaptive moving mesh partial differential equation (MMPDE) method would also improve the accuracy of results by concentrating on the grid nodes in high-gradient regions for transient flows. Applying the CRMWENOZ method alongside MMPDE and using the fifth-order Radau method for time discretization lead to a substantial improvement in the accuracy of simulation, particularly near the liquid–gas interfaces. The accuracy of the proposed hybrid method was compared to other studies’ predictions of one-dimensional (1D) expansion and shock tube problems containing two-phase flow with and without cavitation. The results showed that the hybrid method presented was more accurate than the usual two-phase flow methods while using a reasonable amount of computer resources.

In this paper, we mainly focus on the development of the Taylor-Galerkin/Pressure-Correction method (TG/PC) method to solve the flow of a compressible Newtonian fluid under nonisothermal conditions. The process of development needs applying the two-step Lax–Wendroff method on the energy equation, after which two new steps for energy equations will be obtained within the TG/PC algorithm. In addition, for the density component, the Tait equation of state is adopted to relate density to pressure, which also yields a new step within the novel method to give the correction formula of compressible pressure. To perform the analysis of the new algorithm, Poiseuille flow through axisymmetric rectangular channel for the Newtonian thermal flow is utilized as a simple problem test. The effect of nondimensional factors such as Reynolds number (Re) and Prandtl number (Pr) is discussed in this study. The influence of thermal conductivity $(k)$ and viscosity $(\mu )$ on the solution components is presented as well. Also, comparison for both compressible and incompressible flows is provided in addition to a comparison between both cases’ convergence, as it turns out that the convergence of the incompressible case is better than the compressible case. All the results of the effects presented in this study agree well with the approved physical trend.

This study addressed the compressible flow of viscous fluid in an asymmetric channel under peristalsis. The difference in amplitudes and phase of traveling waves created the asymmetry of channel. Simultaneous effect of magnetic field is also incorporated. Fluid flows through a porous medium. The analytical treatment of the solution is carried out by considering upper wall amplitude as the small parameter. The expressions of flow rate and net axial velocity are constructed for the second-order approximation. Numerical integration is employed to calculate net flow rate. The role of sundry parameters is illustrated graphically. Trapping phenomenon is also taken into account by plotting streamlines against sundry parameters. The significant finding of this study is that flow rate and axial velocity enhance as fluid transitions from hydrodynamic to hydromagnetic. Enhancement in the compressibility parameter trims down the velocity and the flow rate as well. Also, asymmetry of the channel causes an enhancement in the flow rate. This model is the most prevailing version of compressible flow under peristalsis through an asymmetric channel. The findings of this study have worth mentioning yields, which can be applicable in numerous areas of fluid dynamics and aircraft industry.

In this paper we apply the unified coordinate system developed by Hui and his co-workers to the steady compressible flow computation in such a way that the grid is generated physically and automatically. At the beginning of computation one only needs to build a narrow layer of grids near the left boundary. It is demonstrated that by continuously injecting layers of grid in the inflow boundary, the grid will gradually fill up the entire flow domain.

Nonparallel stability of the compressible boundary layers for three-dimensional configurations having large curvature variation on the surface is investigated by using the parabolic stability equations, which are derived from the Navier-Stokes equations in the curvilinear coordinate system. The difference schemes with fourth-order accuracy can be used in the entire computational regions. The global method is combined with the local method using a new iterative formula, thus more precise eigenvalues are obtained, and fast convergences are achieved. Computed curves of the amplification factor and shape functions of disturbances show clearly variable process of the flow stability, and agree well with other available results.

This paper proposes temporal scaling laws of the density-weighted energy spectrum for compressible turbulence in terms of dissipation rate, frequency and the Mach number. The study adopts the incomplete similarity theory in the scaling analysis of compressible turbulence motion. The investigation shows that the temporal Eulerian and Lagrangian energy spectra approach the $-\frac{5}{3}$ and $-2$ power laws when the Mach number M tends to reach unity and infinity, respectively.

This paper deals with construction and convergence analysis of a finite volume scheme for compressible/incompressible (gas–water) flows in porous media. The convergence properties of finite volume schemes or finite element scheme are only known for incompressible fluids. We present a new result of convergence in a two or three dimensional porous medium and under the only consideration that the density of gas depends on global pressure. In comparison with incompressible fluid, compressible fluids requires more powerful techniques; especially the discrete energy estimates are not standard.

Simulations of a flow over a roughness are prohibitively expensive for small-scale structures. If the interest is only on some macroscale quantity it will be sufficient to model the influence of the unresolved microscale effects. Such multiscale models rely on an appropriate upscaling strategy. Here the strategy originally developed by Achdou et al. [Effective boundary conditions for laminar flows over periodic rough boundaries, J. Comput. Phys.147 (1998) 187–218] for incompressible flows is extended to compressible high Reynolds number flow. For proof of concept a laminar flow over a flat plate with partially embedded roughness is simulated. The results are compared with computations on a rough domain.

This work presents a strongly-coupled fluid–structure interaction (FSI) formulation for compressible flows that is developed based on an augmented Lagrangian approach. The method is suitable for handling problems that involve nonmatching fluid–structure interface discretizations. In this work, the fluid is modeled using a stabilized finite element method for the Navier–Stokes equations of compressible flows and is coupled to the structure, which is formulated using isogeometric Kirchhoff–Love shells. The strongly-coupled system is solved using a block-iterative approach. The proposed method is validated using two compressible flow benchmark problems to assess the accuracy of the developed formulation.

In a recent paper (J. Computational Acoustics10 (2002) 387–405) Tam has claimed that the famous Lighthill Acoustic Analogy predicts the wrong flow field for the simple problem of the propagation of a normal shock. However, we show that Tam has misinterpreted the results of his analysis, and that when this error is corrected the results of the Acoustic Analogy are brought into exact agreement with the well-known Rankine–Hugoniot solution of the Euler equations.

Steam or moist air is used as working gas in a wide range of engineering applications of supersonic jets. In these cases, nonequilibrium homogeneous condensation may occur at the downstream of nozzle throat. The surrounding gas will be heated by the release of latent heat of condensation, and may results a change in the flowfield. The present report will describe numerical investigations predicting the effect of nonequilibrium condensation on the flow characteristics of ideally-expanded supersonic free jets. A TVD numerical method is applied to solve RANS and droplet growth equations. The predicted results are compared with the experimental data.

Spontaneous condensation of moist air in supersonic jets is of considerable interest in a variety of natural and industrial processes. During impingement of supersonic moist air jets, the nonequilibrium homogeneous condensation can be experienced at the region between downstream of nozzle exit and an obstacle. The subsequent release of latent heat thus results in a deceleration of the flow and a rise in pressure, known traditionally as the condensation shock; likely have strong effect on the flow features. The present paper reported of the effect of spontaneous nonequilibrium homogeneous condensation of moist air on the aerodynamic and oscillatory flow features of supersonic jets impinging on cavity. A total variation diminishing (TVD) scheme was used to solve the time dependent Favre averaged Navier–Stokes equations, and the droplet growth equation of liquid phase production for simulating the condensing jets. Both qualitative and quantitative validations of the numerical model were accomplished, and the results showed a good agreement between the computed results and experimental data. Predicted flow and oscillatory features of jets were presented.

In this paper, we present a hybrid immersed boundary method (HIBM) for the simulation of two- and three-dimensional compressible viscous flows around stationary and moving obstacles. The proposed approach combines the compressible boundary condition-enforced IBM proposed by Qiu et al. and the Brinkman penalization methods. The boundary condition-enforced IBM uses a fractional step approach alongside a Dirac delta function to satisfy the boundary conditions on the body surface. Although this method works properly in subsonic regimes, it cannot correctly simulate the wake region for a supersonic flow. On the other hand, the penalization method considers the body as a porous media with a low permeability that forces the velocity and energy inside the body to converge to the body velocity and energy. However, unlike the boundary condition-enforced IBM, the streamlines penetrate the body. In the present approach, the positive features of the above-mentioned methods were included and their drawbacks were excluded. The proposed approach was applied using the finite volume method and an E-CUSP scheme. The performance of the proposed method was numerically evaluated in simulating compressible fluid flow around both stationary and moving boundaries, showing a close agreement with other numerical and experimental data available in the literature. Further, the effects of geometry, Reynolds, and Mach numbers were investigated on the supersonic flow field around elliptical cylinders of various aspect ratios. The results revealed that increasing the aspect ratio led to an increase in the shock standoff distance, recirculation zone, and drag coefficient.

The present study is focused on the numerical simulation of pressure wave propagation through the cavitating compressible liquid flow, its interaction with cavitation bubble and the resulting unsteady cavitation evolution. The compressibility effects of liquid water are taken into account and the cavitating flow is governed by one-fluid cavitation model which is based on the compressible Euler equations with the assumption that the cavitation is the homogeneous mixture of liquid and vapour which are locally under both kinetic and thermodynamic equilibrium. Several aspects of the method employed to solve the governing equations are outlined. The unsteady features of cavitating flow due to the external perturbation, such as the cavitation deformation and collapse and consequent pressure increase are resolved numerically and discussed in detail. It is observed that the cavitation bubble collapse is accompanied by the huge pressure surge of order of 100 bar, which is thought to be responsible for the material erosion, noise, vibration and loss of efficiency of operating underwater devices.

The unsteady features of supercavitation disturbed by an introduced pressure wave are investigated numerically using a one-fluid cavitation model. The supercavitating flow is assumed to be the homogeneous mixture of liquid and vapour which are locally under both kinetic and thermodynamic equilibrium. The compressibility effects of liquid water are taken into account to model the propagation of pressure wave through flow and its interaction with supercavitation bubble. The interaction between supercavity enveloping an underwater flat-nose cylinder and pressure wave is simulated and the resulting unsteady behavior of supercavitation is illustrated. It is observed that the supercavity will become unstable under the impact of the pressure wave and may collapse locally, which depends on the strength of perturbation. The huge pressure surge accompanying the collapse of supercavitation may cause the material erosion, noise, vibration and efficiency loss of operating underwater devices.

In this research, a Computational Fluid Dynamics (CFD) technique was used to investigate the effect of choking on the flow and heat transfer characteristics of a typical micro-channel heat sink. Numerical simulations have been carried out using Spalart–Allmaras model. Comparison of the numerical results for the heat transfer rate, mass flow rate and Stanton number with the experimental data were conducted. Relatively good agreement was achieved with maximum relative error 16%, and 8% for heat transfer and mass flow rate, respectively. Also, average relative error 9.2% was obtained for the Stanton number in comparison with the experimental values. Although, the results show that the majority of heat was transferred in the entrance region of the channel, but the heat transfer in micro-channels can also be affected by choking at channel exit. Moreover, the results clearly show that, the location where the flow is choked (at the vicinity of the channel exit) is especially important in determining the heat transfer phenomena. It was found that Spalart–Allmaras model is capable to capture the main features of the choked flow. Also, the effects of choking on the main characteristics of the flow was presented and discussed.

This paper provides a users' guide to a new, general finite difference method for the numerical solution of systems of convection dominated conservation laws. We include both extensive motivation for the method design, as well as a detailed formulation suitable for direct implementation.

Essentially Non-Oscillatory (ENO) methods are a class of high accuracy, shock capturing numerical methods for hyperbolic systems of conservation laws, based on upwind biased differencing in local characteristic fields. The earliest ENO methods used control volume discretizations, but subsequent work [12] has produced a simpler finite difference form of the ENO method. While this method has achieved excellent results in a great variety of compressible flow problems, there are still special situations where noticeable spurious oscillations develop. Why this occurs is not always understood, and there has been no elegant way to eliminate these problems.

Based on the extensive work of Donat and Marquina [1], it appears that these difficulties arise from using a single transformation to local characteristic variables at cell walls in the course of computing wall fluxes. In concrete terms this is the practice of evaluating the flux Jacobian matrix at cell walls using an average of adjacent cell states, such as the Roe average or linear average. When the states differ greatly across the cell wall, using such an intermediate state in the transformation adds subtle spurious features to the solution. As an alternative, Donat and Marquina recommend obtaining the wall flux from a splitting procedure based on fluxes computed separately from the left and right sides. This approach avoids introducing artificial intermediate states, and seems to improve the robustness of many characteristic based methods.

Applying their splitting in the ENO framework, the left and right sided fluxes are evaluated by the ENO interpolation technique, i.e. using the smoothest high order interpolations from each side. In the resulting method, the spurious oscillations are eliminated without sacrificing high resolution. Thus this seems to be an ideal scheme for general hyperbolic systems: it provides high accuracy and shock capturing without numerical artifacts, problem dependent "fixes", or free parameters that must be "tuned". (Of course, for scalar equations this "fix" is unnecessary and nonexistent.)

This paper is intended as a self-contained guide to this new approach, in the context of solving general systems of convection-diffusion-reaction conservation laws. We provide all the conceptual background needed to understand the design of numerical methods for systems of hyperbolic conservation laws in general, and the finite difference ENO method and Marquina's flux splitting procedure in particular. We then give a detailed presentation of the preferred form of ENO with Marquina's splitting. We conclude with one example where this eliminates a severe, non-physical oscillation in a complicated ENO based calculation.