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The computation of compressible coaxial jets has moved into the field of interest not only in fundamental research but also in industrial applications, especially in chemical engineering. Numerical simulations of such flows are performed here, using a code specifically developed for gaseous turbulent flows which can also take into account chemical reactions. The coaxial jet can be regarded as a model of injection device in industrial applications; one can cite combustion and aeroacoustics technology. Three-dimensional numerical simulations in this configuration, already published by various authors in open literature are limited to incompressible isothermal flow. In our work, we have explicitly taken into account the temperature gradient effects on the dynamics and mixing mechanisms. Indeed, we have investigated a spatially developing compressible (isothermal and non-isothermal coaxial jet). The numerical model is based on time and space resolutions of compressible Navier-Stokes equations. The piecewise parabolic method (PPM) is combined with a linearized Riemann solver. This scheme adds non-linear dissipation intermittently just where and when needed in order to avoid spurious oscillations and guarantee monotonicity for the advection equation. The simulation can, therefore, be regarded as large-Eddy simulations: large scales are accurately solved with minimal viscosity and non-linear dissipation extracts energy out of the small scales in order to avoid non-physical oscillations. In order to study the mixing between Air-Air flows, we consider the mixture fraction f to track the mixing between two species seeded in the coaxial jets. A great attention is paid to the spatial-temporal evolution of the mixture fraction f , with a particular interest to probability density function. The comparison between the numerical results and experimental data is fairly good, with respect to the mean and turbulent fields. We found that the inner potential core length in the non-isothermal configuration reduced with respect to the isothermal coaxial jet due to the gradient of temperature. It was shown that in the non-isothermal coaxial jet, the temperature gradient leads to the rapid development of the inner Kelvin-Helmholtz vortices implying an efficient mixing of the species close to the exit of the computational domain. • The approach employed is based on Monotonic Integrated Large Eddy Simulation. • The potential cores length of the coaxial jets depends strongly on the temperature gradients. • The temperature gradient leads to the rapid development of the inner Kelvin-Helmholtz vortices. • The turbulent mixing becomes more homogeneous in the case of the non-isothermal jet. [ABSTRACT FROM AUTHOR]

The recently proposed boundary condition-enforced immersed boundary-gas kinetic flux solver (IB-GKFS) is a new approach for simulation of compressible flows with curved and moving boundaries. In the previous application of IB-GKFS, only the Dirichlet boundary condition is considered, which cannot be applied directly to the Neumann boundary condition. In this paper, an auxiliary layer of Lagrangian points is introduced to tackle Neumann boundary condition. Two test cases, including flow around a circular cylinder and flow around a NACA0012 airfoil, are carried out for validation. The results obtained by the present scheme are compared with the reference data available in the literature. Good agreements are achieved, which indicate that the developed method can effectively simulate the compressible flow with Neumann boundary condition. [ABSTRACT FROM AUTHOR]

A focused laser can cause local optical breakdown of a gas, which leads to rapid deposition of energy into a high-temperature plasma kernel that expands and induces a complex flow. For some conditions, hot gas is rapidly ejected along the laser axis up to distances several times the kernel size, with a particularly curious feature: relatively small changes in, for example, initial pressure can cause the direction of this ejection to reverse. Detailed axisymmetric simulations of a model energy kernel in an inert gas provide a hydrodynamic description of this phenomenon, reproducing key observations in corresponding experiments, including the vortex-ring-like features that constitute the ejection. These simulations are analysed to show how changes in the early-time kernel can lead to ejection or its reversal via alteration in the relative strength and position of the vorticity produced. A corresponding semi-infinite geometry is used to isolate two mechanisms: vorticity production by the generated shock and by baroclinic torque at the kernel boundary. Dependence on the initial kernel asymmetry is quantified, as it ultimately determines whether the vorticity, upon its subsequent evolution, develops into the ring-like structure that ejects. Even simple elongation of the energy kernel alone can reverse the direction. [ABSTRACT FROM AUTHOR]

This article shows the importance of flow compressibility on the heat transfer in confined impinging jets, and how it is driven by both the Mach number and the wall heat flux. Hence, we present a collection of cases at several Mach numbers with different heat-flux values applied at the impingement wall. The wall temperature scales linearly with the imposed heat flux and the adiabatic wall temperature is found to be purely governed by the flow compression. Especially for high heat-flux values, the non-constant wall temperature induces considerable differences in the thermal conductivity of the fluid. This phenomenon has to date not been discussed and it strongly modulates the Nusselt number. In contrast, the heat transfer coefficient is independent of the varying thermal properties of the fluid and the wall heat flux. Furthermore, we introduce the impingement efficiency, which highlights the areas of the wall where the temperature is influenced by compressibility effects. This parameter shows how the contribution of the flow compression to raising the wall temperature becomes more dominant as the heat flux decreases. Thus, knowing the adiabatic wall temperature is indispensable for obtaining the correct heat transfer coefficient when low heat-flux values are used, even at low Mach numbers. Lastly, a detailed analysis of the dilatation field also shows how the compressibility effects only affect the heat transfer in the vicinity of the stagnation point. These compressibility effects decay rapidly further away from the flow impingement, and the density changes along the developing boundary layer are caused instead by variable inertia effects. [ABSTRACT FROM AUTHOR]

A typical weighted compact nonlinear scheme (WCNS) uses a convex combination of several low-order polynomials approximated over selected candidate stencils of the same width, achieving non-oscillatory interpolation near discontinuities and high-order accuracy for smooth solutions. In this paper, we present a new multi-resolution fifth-order WCNS by making use of the information of polynomials on three nested central spatial sub-stencils having first-, third- and fifth-order accuracy, respectively. The new scheme is capable of obtaining high-order spatial interpolation in smooth regions, and it is characterised by the feature of gradually degrading from fifth-order down to first-order accuracy as large stencils deemed to be crossing strong discontinuities. The advantages of the present scheme include the superior resolution for high-wavenumber fluctuations and the flexibility of implementing different numerical flux functions. [ABSTRACT FROM AUTHOR]

The immersed boundary method is a methodology for dealing with boundary conditions at fluid–fluid and fluid–solid interfaces. The immersed boundary method has been attracting growing attention in the recent years due to its simplicity in mesh processing. Great effort has been made to develop its new features and promote its applications in new areas. This review is focused on assessing the immersed boundary method fundamentals and the latest progresses especially the strategies to address the challenges and the applications of the immersed boundary method. Various numerical examples are also presented for demonstrating the capability of the immersed boundary method, including blood flow and blood cells, flapping flag, flow around a hoverfly, turbulence flow over a wavy boundary, shock wave-induced vibration, and acoustic waves scattered by a cylinder and a sphere. The major challenges and several open issues in this field are highlighted. [ABSTRACT FROM AUTHOR]

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We develop a new formulation for the computational modeling of underwater explosions (UNDEX). The formulation is based on the Navier–Stokes equations of compressible flows augmented with the species mass conservation equations. We develop a stabilized formulation with discontinuity capturing for this multiphase model using the framework of advective–diffusive systems. Isogeometric Analysis is successfully employed to discretize the resulting stabilized formulation. Novel interface sharpening and mass correction procedures are also developed based on the invertible mapping between the level-set and volume fraction functions. Several numerical examples of increasing complexity and including experimental validation are presented in order to demonstrate the good performance of the new UNDEX modeling methodology. [ABSTRACT FROM AUTHOR]

This article is dedicated to the construction of a robust and accurate numerical scheme based on the lattice Boltzmann method (LBM) for simulations of gaseous detonations. This objective is achieved through careful construction of a fully conservative hybrid lattice Boltzmann scheme tailored for multi-species reactive flows. The core concept is to retain LBM low dissipation properties for acoustic and vortical modes by using the collide and stream algorithm for the particle distribution function, while transporting entropic and species modes via a specifically designed finite-volume scheme. The proposed method is first evaluated on common academic cases, demonstrating its ability to accurately simulate multi-species compressible and reactive flows with discontinuities: the convection of inert species, a Sod shock tube with two ideal gases and a steady one-dimensional inviscid detonation wave. Subsequently, the potential of this novel approach is demonstrated in one- and two-dimensional inviscid unsteady gaseous detonations, highlighting its ability to accurately recover detonation structures and associated instabilities for high activation energies. To the authors' knowledge, this study is the first successful simulation of detonation cellular structures capitalizing on the LBM collide and stream algorithm. [ABSTRACT FROM AUTHOR]

A kinetic energy and entropy preserving (KEEP) finite-volume scheme on unstructured meshes is proposed for non-dissipative and stable compressible flow computations. The KEEP finite volume scheme proposed in the present study is based on the existing KEEP schemes developed for finite difference methods. The KEEP schemes have shown superior numerical robustness without numerical dissipation in previous studies. The KEEP schemes are discretized such that the numerical fluxes discretely replicate the key analytical relations that the governing equations hold, leading to preservation of kinetic energy and a superior entropy preservation property in the incompressible and inviscid limits. This study proposes using cell-vertex discretization for the proposed KEEP finite volume scheme in order to maintain this characteristic property of the KEEP scheme and achieve second-order accuracy in space on simplex meshes and arbitrary meshes that are not highly irregular. In the numerical tests performed in this study, the proposed KEEP finite volume scheme successfully performs long-time stable computations on various unstructured meshes. Also, the proposed KEEP scheme shows much better numerical stability and spatial accuracy than the KEEP scheme with cell-centered discretization. • Superior kinetic energy and entropy preservation property. • Cell-vertex finite volume discretization for second-order accuracy. • Stable and non-dissipative computations on unstructured meshes. [ABSTRACT FROM AUTHOR]

A continuous forcing immersed boundary method (IBM) and a volume penalization method are investigated to simulate compressible viscous flows past an isothermal or adiabatic solid obstacle using a body non-conformal Cartesian grid. The present methods are validated on a large range of flow configurations such as incompressible and compressible flows (steady or unsteady) past isothermal or adiabatic solid obstacles. An adiabatic condition with implicit treatment of the source term is derived for the penalization method, taking advantage of the framework of the ghost-cell methods. Accuracy and computational cost of the methods are discussed. Three-dimensional supersonic flow configurations are carried out with the penalization method. The coupling between the porosity parameter and the different boundary conditions of the present penalization method is investigated in order to properly reproduce the wave reflection on a solid wall. Finally, a new penalization model is designed to improve the shock wave reflection on a solid surface while significantly reducing the computational cost compared to the previous porosity model. • A rigorous comparison of the performance of two IBM methods is conducted. • Both Dirichlet and Neumann thermal boundary conditions are implemented and validated. • An improvement of the volume penalization method is proposed for cases involving shock waves impact. • The volume penalization method is found to be accurate and efficient to solve compressible flows. [ABSTRACT FROM AUTHOR]

Summary: We have developed a fundamentally new type of simple lattice Boltzmann (LB) model for the compressible Navier‐Stokes equations based on the kinetic system proposed by Sone. The model uses the kinetic equation of free‐molecular type in the streaming process and modifies the distribution function to its Chapman‐Enskog type at each time step. Compared with the current LB models, the proposed model is superior in the following two points: (i) there are no inherent errors associated with the Knudsen number; (ii) any flow parameters, including three transport coefficients, can be chosen freely according to our convenience. Numerical tests and error estimates confirm the above statements. [ABSTRACT FROM AUTHOR]

• A thermal LB model has been developed on standard lattices for subsonic to sonic compressible flows. • An extension of the Hybrid Recursive Regularized (HRR) collision model is developed for compressible flows. • The defect of Galilean invariance and non-hydrodynamic oscillation is effectively eliminated by HRR collision model. • Excellent agreement is shown for the simulation of compressible laminar flow over flat plate, as well as isentropic vortex convection. A thermal lattice Boltzmann model with a hybrid recursive regularization (HRR) collision operator is developed on standard lattices for simulation of subsonic and sonic compressible flows without shock. The approach is hybrid: mass and momentum conservation equations are solved using a lattice Boltzmann solver, while the energy conservation is solved under entropy form with a finite volume solver. The defect of Galilean invariance related to Mach number is corrected by the third order equilibrium distribution function, supplemented by an additional correcting term and hybrid recursive regularization. The proposed approach is assessed considering the simulation of i) an isentropic vortex convection, ii) a two dimensional acoustic pulse and iii) non-isothermal Gaussian pulse with Ma number in range of 0 to 1. Numerical simulations demonstrate that the flaw in Galilean invariance is effectively eliminated by the compressible HRR model. At last, the compressible laminar flows over flat plate at Ma number of 0.3 and 0.87, Reynolds number of 105 are considered to validate the capture of viscous and diffusive effects. [ABSTRACT FROM AUTHOR]

In order to simulate the compressible and incompressible turbulent flows, a gas-kinetic scheme (GKS) based on the Bhatnagar–Gross–Krook (BGK) model coupled with the shear stress transport (SST) two-equation turbulence model is developed. The SST model is a two-equation eddy-viscosity model based on the k − ω and k − ε models, which is one of the most common turbulence models and widely used in Reynolds averaged Navier–Stokes (RANS) modeling for turbulent flows. In this study, we implement GKS–SST coupling model by (a) solving the GKS and SST models in vertex-based finite volume method on hybrid grids; (b) incorporating the SST model into the GKS based on the eddy viscosity hypothesis and using the eddy viscosity to modify the collision time in gas-kinetic scheme; (c) using a modified Venkatakrishnan limiter for hybrid and highly stretched grids during the initial reconstruction stage; (d) applying the boundary conditions adopted from vertex-based solvers for Navier–Stokes equations in present GKS solver. The original gas-kinetic scheme has been proved to be an accurate and effective approach for incompressible and compressible laminar flows, and the SST turbulence model is incorporated here for the turbulent flow. The eddy viscosity at the cell centers is obtained by solving SST model, and then the eddy viscosity on the cell interface can be interpolated from cell centers around. Numerical experiments performed on high Reynolds number turbulent flows around the 2D zero pressure gradient flat plate and a RAE2822 airfoil demonstrate the applicability of the GKS–SST model presented in this study for simulations of high Reynolds number turbulent flows. [ABSTRACT FROM AUTHOR]

We present a new high-order Lagrangian discontinuous Galerkin (DG) hydrodynamic method for gas and solid dynamics. The evolution equations for specific volume, momentum, and total energy are discretized using the modal DG approach. The specific volume, velocity, and specific total energy fields are approximated with up to quadratic Taylor series polynomials. The specific internal energy, pressure, and stress deviators are nodal quantities. The stress deviators are evolved forward in time using a hypoelastic–plastic approach, which requires a velocity gradient. A new method is presented for calculating a high-order polynomial for the velocity gradient in an element. Plasticity is handled by applying a radial return model to the stress deviators. Limiting approaches are presented for modal and nodal fields. The TVD RK time integration method is used to temporally advance all governing evolution equations. Generalized Lagrangian DG equations are derived but test problems are calculated for 1D Cartesian coordinates. A suite of gas and solid dynamics test problem results are calculated to demonstrate the stability and formal accuracy of the new Lagrangian DG method. [ABSTRACT FROM AUTHOR]

• The evolution of gas-dynamic flow affects the ignition process in the shock tube. • The non-steady flow dynamics determines the origins of ignition kernels. • The reaction wave is forming at the background of non-uniform flow field. • The detonation arises as a result of transient behavior of reaction wave. The paper analyses in details and describes the process of ignition kernel formation and subsequent detonation onset behind the shock wave propagating in the shock tube. To get the overall pattern of the process a series of one- and two-dimensional calculations are carried out with the use of a dissipation-free numerical technique. It is shown that one of the leading roles in the process of ignition kernel formation belongs to the non-steady flow dynamics establishing behind the shock wave. The development of the boundary layer determines both the temperature re-distribution in the near-wall region and the conditions for gas-dynamic acceleration of the flow. With an account of thermal runaway, the most intensively heated region corresponds to the area between the inner margin of the boundary layer and the contact surface separating driver gas and the test mixture. After localized ignition takes place the forming reaction wave propagates out from the ignition epicenter. Reaction wave propagates behind the outrunning compression wave through the already reacting mixture. Shock-induced compression of the test mixture provides conditions for the self-sustained acceleration of the combustion wave, and finally, the detonation onset takes place. [ABSTRACT FROM AUTHOR]

Abstract A genuinely two-dimension Riemann solver for compressible flows in curvilinear coordinates is proposed. Following Balsara's idea, this two-dimension solver considers not only the waves orthogonal to the cell interfaces, but also those transverse to the cell interfaces. By adopting the Toro–Vasquez splitting procedure, this solver constructs the two-dimensional convective flux and the two-dimensional pressure flux separately. Systematic numerical test cases are conducted. One dimensional Sod shock tube case and moving contact discontinuity case indicate that such two-dimensional solver is capable of capturing one-dimensional shocks, contact discontinuities, and expansion waves accurately. Two-dimensional double Mach reflection of a strong shock case shows that this scheme is with a high resolution in Cartesian coordinates. Also, it is robust against the unphysical shock anomaly phenomenon. Hypersonic viscous flows over the blunt cone and the two-dimensional Double-ellipsoid cases show that the two-dimensional solver proposed in this manuscript is with a high resolution in curvilinear coordinates. It is promising to be widely used in engineering areas to simulate compressible flows. Highlights • A novel genuinely two-dimensional Riemann solver for compressible flows is proposed. • This scheme is originally constructed in curvilinear coordinates. • This scheme is with a high level of accuracy in simulating multi-dimensional complex flows. [ABSTRACT FROM AUTHOR]

We present an immersogeometric analysis (IMGA) approach for the simulation of compressible flows around complex geometries. In this method, compressible flow simulations are performed directly on various boundary representations (B-reps) of mechanical designs, circumventing the labor-intensive and time-consuming cleanup of complex geometric models. A new formulation for the weak imposition of essential boundary conditions in the context of non-body-fitted meshes is proposed. The formulation employs the non-symmetric Nitsche method, which yields good performance especially when the penalty parameters are difficult to estimate. We test the proposed immersogeometric formulation on benchmark problems for a wide range of Reynolds and Mach numbers, showing its robustness and accuracy. Finally, the methodology is applied to the simulation of a UH-60 Black Hawk helicopter in forward flight, illustrating the ability of the proposed approach to support the design of real-world engineering systems through high-fidelity aerodynamic analysis. [ABSTRACT FROM AUTHOR]

Experiments and numerical analyses were conducted to investigate the reflection and shielding effects of jet noise by a horizontal tail and an aft-mounted engine. An acoustic test using a cold jet at a Mach number of 0.98 was carried out with a 28.8-mm-diameter exhaust nozzle and a T-tail model. The effects of the position and angle of the horizontal tail were investigated using the boundary element method and a fitted jet noise source model. The experimental results showed that the sound pressure level increased by 1.5 dB in the downward direction of the aircraft at a Strouhal number of 0.94. The numerical analysis results showed that the reflection effect was highly dependent on the relative position and size of the horizontal tail, the location of the source, and the angle of the horizontal tail. In addition, the effect of the reflected direction was ascertained to find an appropriate horizontal tail and engine arrangement that reduces noise. It was found that the greatest influence in terms of the effective perceived noise level occurred when the reflected direction was 60° from the jet axis. [ABSTRACT FROM AUTHOR]

• We carry out direct numerical simulation of supersonic pipe flow up to Re τ = 1000. • We verify the predictive power of compressibility transformations for mean velocity and Reynolds stresses, by also comparing with available incompressible DNS data at matching Reynolds number. • We study scaling laws for the streamwise velocity spectra in the outer part of the wall layer, to quantify compressibility effects on the turbulent eddies. • We study the statistics of scalar fields passively advected by the fluid, with special emphasis on identifying similarities and differences with respect to the velocity field. We study compressible turbulent flow in a circular pipe at computationally high Reynolds number. Classical related issues are addressed and discussed in light of the DNS data, including validity of compressibility transformations, velocity/temperature relations, passive scalar statistics, and size of turbulent eddies. Regarding velocity statistics, we find that Huang's transformation yields excellent universality of the scaled Reynolds stresses distributions, whereas the transformation proposed by Trettel and Larsson (2016) yields better representation of the effects of strong variation of density and viscosity occurring in the buffer layer on the mean velocity distribution. A clear logarithmic layer is recovered in terms of transformed velocity and wall distance coordinates at the higher Reynolds number under scrutiny (Re τ ≈ 1000), whereas the core part of the flow is found to be characterized by a universal parabolic velocity profile. Based on formal similarity between the streamwise velocity and the passive scalar transport equations, we further propose an extension of the above compressibility transformations to also achieve universality of passive scalar statistics. Analysis of the velocity/temperature relationship provides evidence for quadratic dependence which is very well approximated by the thermal analogy proposed by Zhang et al. (2014). The azimuthal velocity and scalar spectra show an organization very similar to canonical incompressible flow, with a bump-shaped distribution across the flow scales, whose peak increases with the wall distance. We find that the size growth effect is well accounted for through an effective length scale accounting for the local friction velocity and for the local mean shear. [ABSTRACT FROM AUTHOR]

• Direct numerical simulation of supersonic square duct flow is performed, up to Re τ = 500. • Classical compressibility transformations for velocity, developed for plane channel flow and boundary layer, are extended to the case of multiple walls. • The accuracy of temperature-velocity relations for square duct flow is studied. • The transport of a passive scalar field is also considered and the differences with respect to the temperature field are analyzed. We carry out direct numerical simulation of compressible square duct flow in the range of bulk Mach numbers M b = 0.2 − 3 , and up to friction Reynolds number Re τ = 500. The effects of flow compressibility on the secondary motions are found to be negligible, with the typical Mach number associated with the cross-stream flow always less than 0.1. As in the incompressible case, we find that the wall law for the mean streamwise velocity applies with good approximation with respect to the nearest wall, upon suitable compressibility transformation. The same conclusion also applies to a passive scalar field, whereas the mean temperature does not exhibit inertial layers because of nonuniformity of the aerodynamic heating. We further find that the same temperature/velocity relation that holds for planar channels is applicable with good approximation for square ducts, and develop a similar relation between temperature and passive scalars. [ABSTRACT FROM AUTHOR]

This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displacements on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations was proposed in previous works, which removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, preserve the initial quality of the mesh throughout the simulation. We propose to integrate an Arbitrary Lagrangian Eulerian compressible flow solver into this process to demonstrate its capabilities in a full CFD computation context. This solver relies on a local enforcement of the discrete geometric conservation law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid–structure interaction (FSI). In the latter case, the six degrees of freedom approach for rigid bodies is considered. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations. [ABSTRACT FROM AUTHOR]

An analytical model is presented for the configuration of Mach reflection (MR) due to the interaction of two-dimensional steady supersonic flow over asymmetric wedges. The present asymmetric MR model is an extension of an earlier model for the symmetric MR configuration. The overall Mach reflection (oMR) in the asymmetric wedge configuration is analysed as a combination of upper and lower half-domains of symmetric reflection configurations. Suitable assumptions are made to close the combined set of equations. The subsonic pocket downstream of the Mach stem is taken to be oriented along an average inclination, based on the streamline deflections by the Mach stem at the triple points. This assumption is found to give satisfactory results for all types of oMR configurations. The oMR configuration is predicted for all types of reflections such as direct Mach reflection (DiMR), stationary Mach reflection (StMR) and inverse Mach reflection (InMR). The reflection configuration and Mach stem shape given by the model for various sets of wedge angles, especially those giving rise to InMR, have been predicted and validated with the available numerical and experimental data. The von Neumann criterion for oMR is accurately predicted by this model. The asymmetric Mach stem profile is well captured. The variation of Mach stem height with wedge angle is also analysed and it is found that simplification of an asymmetric MR to a symmetric MR leads to over-prediction of the Mach stem height and hence the extent of the subsonic region. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a third-order reconstructed DG(p 1 p 2) method based on the variational reconstruction (VR) (Wang et al., 2017 [24]) is developed for simulating the two dimensional steady-state compressible flows on unstructured and hybrid grids. The proposed method combines the advantages of the DG discretization with the flexibility of the variational reconstruction, which exhibits its superior potential in enhancing the level of accuracy compared to the underlying DG method. In this variational rDG(p 1 p 2) method, the low order degrees of freedom are evolved through the underlying DG(p 1) method, while the high order degrees of freedom are reconstructed through the variational reconstruction, in which the constitutive relations are built by minimizing the so-called 'cost function'. The cost function is defined by the total interfacial jump integration in the computational domain using the variational method. The large sparse linear system resulted by the variational reconstruction is solved in an efficient way coupled with the temporal discretization for the steady-state simulations. A number of test cases are presented to assess the performance of the new high order variational rDG(p 1 p 2) method. [ABSTRACT FROM AUTHOR]

The development of a non-periodic $\text{air}\text{/}\text{SF}_{6}$ gaseous interface subjected to a planar shock wave is investigated experimentally and theoretically to evaluate the effects of the non-periodic portions of the interface on the Richtmyer–Meshkov instability. Experimentally, five kinds of discontinuous chevron-shaped interfaces with or without non-periodic portions are created by the extended soap film technique. The post-shock flows and the interface morphologies are captured by schlieren photography combined with a high-speed video camera. A periodic chevron-shaped interface, which is multi-modal (81 % fundamental mode and 19 % high-order modes), is first considered to evaluate the impulsive linear model and several typical nonlinear models. Then, the non-periodic chevron-shaped interfaces are investigated and the results show that the existence of non-periodic portions significantly changes the balanced position of the initial interface, and subsequently disables the nonlinear model which is applicable to the periodic chevron-shaped interface. A modified nonlinear model is proposed to consider the effects of the non-periodic portions. It turns out that the new model can predict the growth of the shocked non-periodic interface well. Finally, a method is established using spectrum analysis on the initial shape of the interface to separate its bubble structure and spike structure such that the new model can apply to any random perturbed interface. These findings can facilitate the understanding of the evolution of non-periodic interfaces which are more common in reality. [ABSTRACT FROM AUTHOR]

The deformation of the Mach stem in pseudo-steady shock wave reflections is investigated numerically and theoretically. The numerical simulation provides the typical flow patterns of Mach stem deformation and reveals the differences caused by high-temperature gas effects. The results also show that the wall jet, which causes Mach stem deformation, can be regarded as a branch of the mainstream from the first reflected shock. A new theoretical model for predicting the Mach stem deformation is developed by considering volume conservation. The theoretical predictions agree well with the numerical results in a wide range of test conditions. With this model, the wall-jet velocity and the inflow velocity from the Mach stem are identified as the two dominating factors that convey the influence of high-temperature thermodynamics. The mechanism of high-temperature gas effects on the Mach stem deformation phenomenon are then discussed. [ABSTRACT FROM AUTHOR]

Abstract This paper concerns a study of pressure fluctuations beneath hypersonic transitional and turbulent boundary layers and associated acoustic loading on a flat surface. We have employed high-order implicit large eddy simulations in conjunction with the atmospheric (von Kármán) multimode energy spectrum as initial condition, and conducted simulations at Mach 4, 6 and 8 and for different inflow turbulence intensities. The spectral analysis of the pressure fluctuations shows consistent results with the available theoretical, experimental and numerical data for fully turbulent boundary layers. In the transition region the spectrum roll-off diverges from the existing scaling predictions for incompressible, as well as fully-turbulent compressible flows. This study shows that the spectrum in the transition region is governed by different scaling laws. The Mach number has a direct impact on the spectrum for both transitional and fully turbulent flows, especially in the high-frequency region of the spectrum. Increasing the inlet turbulence intensity leads to higher amplitude pressure fluctuations in the mid-to-high-frequency region, faster transition to turbulence, and higher acoustic loading on the solid surface. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive investigation into flow past a circular cylinder where compressibility and rarefaction effects play an important role. The study focuses on steady subsonic flow in the Reynolds-number range 0.1-45. Rarefaction, or non-equilibrium, effects in the slip and early transition regime are accounted for using the method of moments and results are compared to data from kinetic theory obtained from the direct simulation Monte Carlo method. Solutions obtained for incompressible continuum flow serve as a baseline to examine non-equilibrium effects on the flow features. For creeping flow, where the Reynolds number is less than unity, the drag coefficient predicted by the moment equations is in good agreement with kinetic theory for Knudsen numbers less than one. When flow separation occurs, we show that the effects of rarefaction and velocity slip delay flow separation and will reduce the size of the vortices downstream of the cylinder. When the Knudsen number is above 0.028, the vortex length shows an initial increase with the Reynolds number, as observed in the standard no-slip continuum regime. However, once the Reynolds number exceeds a critical value, the size of the downstream vortices decreases with increasing Reynolds number until they disappear. An existence criterion, which identifies the limits for the presence of the vortices, is proposed. The flow physics around the cylinder is further analysed in terms of velocity slip, pressure and skin friction coefficients, which highlights that viscous, rarefaction and compressibility effects all play a complex role. We also show that the local Knudsen number, which indicates the state of the gas around the cylinder, can differ significantly from its free-stream value and it is essential that computational studies of subsonic gas flows in the slip and early transition regime are able to account for these strong non-equilibrium effects. [ABSTRACT FROM AUTHOR]

Highlights • Combining multigrid and p-adaptation methods speeds up convergence significantly. • Anisotropic τ -estimation can be performed cheaply in an anisotropic multigrid cycle. • Multi-stage p-adaptation methods based on full multigrid improve performance. Abstract High-order discontinuous Galerkin methods have become a popular technique in computational fluid dynamics because their accuracy increases spectrally in smooth solutions with the order of the approximation. However, their main drawback is that increasing the order also increases the computational cost. Several techniques have been introduced in the past to reduce this cost. On the one hand, local mesh adaptation strategies based on error estimation have been proposed to reduce the number of degrees of freedom while keeping a similar accuracy. On the other hand, multigrid solvers may accelerate time marching computations for a fixed number of degrees of freedom. In this paper, we combine both methods and present a novel anisotropic p-adaptation multigrid algorithm for steady-state problems that uses the multigrid scheme both as a solver and as an anisotropic error estimator. To achieve this, we show that a recently developed anisotropic truncation error estimator [1, A. M. Rueda-Ramírez, G. Rubio, E. Ferrer, E. Valero, Truncation error estimation in the p-anisotropic discontinuous Galerkin spectral element method, J. Sci. Comput.] is perfectly suited to be performed inside the multigrid cycle with negligible extra cost. Furthermore, we introduce a multi-stage p-adaptation procedure which reduces the computational time when very accurate results are required. The proposed methods are tested for the compressible Navier–Stokes equations, where we investigate two steady-state cases. First, the 2D boundary layer flow on a flat plate is studied to assess accuracy and computational cost of the algorithm, where a speed-up of 816 is achieved compared to the traditional explicit method. Second, the 3D flow around a sphere is simulated and used to test the anisotropic properties of the proposed method, where a speed-up of 152 is achieved compared to the explicit method. The proposed multi-stage procedure achieved a speed-up of 2.6 in comparison to the single-stage method in highly accurate simulations. [ABSTRACT FROM AUTHOR]

The objective of this work is to investigate linear modal and algebraic instability in Poiseuille flows with fluids close to their vapour-liquid critical point. Close to this critical point, the ideal gas assumption does not hold and large non-ideal fluid behaviours occur. As a representative non-ideal fluid, we consider supercritical carbon dioxide (CO2) at a pressure of 80 bar, which is above its critical pressure of 73.9 bar. The Poiseuille flow is characterized by the Reynolds number (Re =ρ* w u* r h*/μ* w), the product of the Prandtl (Pr=μ* wC* pw=/* w) and Eckert numbers (Ec=u*2 r=C* pwT* w ) and the wall temperature that in addition to pressure determine the thermodynamic reference condition. For low Eckert numbers, the flow is essentially isothermal and no difference with the well-known stability behaviour of incompressible flows is observed. However, if the Eckert number increases, the viscous heating causes gradients of thermodynamic and transport properties, and non-ideal gas effects become significant. Three regimes of the laminar base flow can be considered: the subcritical (temperature in the channel is entirely below its pseudo-critical value), transcritical and supercritical temperature regimes. If compared to the linear stability of an ideal gas Poiseuille flow, we show that the base flow is modally more unstable in the subcritical regime, inviscid unstable in the transcritical regime and significantly more stable in the supercritical regime. Following the principle of corresponding states, we expect that qualitatively similar results will be obtained for other fluids at equivalent thermodynamic states. [ABSTRACT FROM AUTHOR]

Three-dimensional shock wave reflection comprises flow physics that is significantly different from the well-documented two-dimensional cases in a number of aspects. The most important differentiating factor is the sweep of the shock system. In particular, this work examines the nature of flow fields in which there is a transition of shock reflection configuration in three-dimensional space. The flow fields investigated have been made to exist in the absence of edge effects influencing the shock interaction and transition, as found previously to exist in conventional double-wedge studies. In general, the shock configurations are those with central regular and peripheral Mach reflection portions. It is shown that the sweep angle of the portions on either side of the transition point is subject to a cusp, as per an analytical model that is developed. This is confirmed with the use of numerical models with additional evidence provided by experimental results using oblique shadow photography. Further application of the principles of three-dimensional shock analysis and those pertaining to the sweep cusp model yield important insights regarding the overall shock geometry and that at transition. [ABSTRACT FROM AUTHOR]

In this paper separation-induced shock reflection is studied theoretically and experimentally. An analytical model is proposed to establish the connections among upstream conditions, downstream conditions and shock configurations. Furthermore, the minimum entropy production principle is employed to determine the incident shock angles as well as the criterion for the transition from regular reflection to Mach reflection, which agrees well with experimental results. Additionally, a solution path for a reflected shock that fulfills the minimum entropy production principle is found in the overall regular reflection domain, based on which the steadiest shock configuration may be determined according to upstream and downstream conditions. [ABSTRACT FROM AUTHOR]

Highlights • All-Mach fully conservative formulation using the VOF method. • The formulation includes surface tension and viscous forces. • The new method avoids numerical diffusion of momentum and energy during advection. • The code is tested for various problems involving bubbles in compressible liquids. Abstract This paper presents a generalization of an all-Mach formulation for multiphase flows accounting for surface tension and viscous forces. The proposed numerical method is based on the consistent advection of conservative quantities and the advection of the color function used in the Volume of Fluid method avoiding any numerical diffusion of mass, momentum and energy across the interface during the advection step. The influence of surface tension and liquid compressibility on the dynamic response of the bubbles is discussed by comparing the full 3D solution with the predictions provided by the Rayleigh–Plesset equation for two relevant problems related to the dynamic response of bubbles to pressure disturbances: The linear oscillation of a single bubble in an acoustic field and the Rayleigh collapse problem. Finally, the problem of the collapse of a bubble close to a wall is compared with experimental results showing the robustness of the method to simulate the collapse of air bubbles in liquids in problems where bubbles generate a high velocity liquid jet. [ABSTRACT FROM AUTHOR]

Abstract The development of an improved IBM method is proposed in the present article. This method roots in efficient proposals developed for the simulation of incompressible flows, and it is expanded for compressible configurations. The main feature of this model is the integration of a pressure-based correction of the IBM forcing which is analytically derived from the set of dynamic equations. The resulting IBM method has been integrated in various flow solvers available in the CFD platform OpenFOAM. A rigorous validation has been performed considering different test cases of increasing complexity. The results have been compared with a large number of references available in the literature of experimental and numerical nature. This analysis highlights numerous favorable characteristics of the IBM method, such as precision, flexibility and computational cost efficiency. Highlights • A pressure-based correction for IBM analytically derived from the set of equations. • The developed IBM dramatically improves near wall pressure prediction. • The pressure-corrected IBM exhibited a high level of algorithmic flexibility. • The IBM formulation is efficient with respect to the computational costs demanded. [ABSTRACT FROM AUTHOR]

Mach reflection in steady supersonic flow with two incident shock waves is studied. The second incident shock wave is produced by an additional deflection of the wedge lower surface, at some point ensuring that the two incident shock waves would intersect at the reflecting surface in case of normal reflection. Both theory and computational fluid dynamics (CFD) are used to study the flow structure and the influence of the second incident shock wave. The overall flow configuration, in case of Mach reflection, is shown to be composed of a triple shock structure, a shock/shock interaction structure and a shock/slipline reflection structure. Similar phenomenon, triggered by a high downstream pressure, has been observed before numerically, but not studied theoretically. The second incident shock wave reflects over the slipline to deflect the slipline more towards the reflecting surface, increasing thus the Mach stem height, advancing the transition of regular reflection to Mach reflection of the first incident shock wave, and causing an inverted Mach reflection below the usual von Neumann condition. A Mach stem height model built for a weak second incident shock wave is used to study the influence of the second incident shock wave on the Mach stem height. Both theory and CFD predict a maximum of the Mach stem height at some additional wedge deflection angle. [ABSTRACT FROM AUTHOR]

Experimental evidence is provided to demonstrate that the upstream-travelling waves in two jets screeching in the A1 and A2 modes are not free-stream acoustic waves, but rather waves with support within the jet. Proper orthogonal decomposition is used to educe the coherent fluctuations associated with jet screech from a set of randomly sampled velocity fields. A streamwise Fourier transform is then used to isolate components with positive and negative phase speeds. The component with negative phase speed is shown, by comparison with a vortex-sheet model, to resemble the upstream-travelling jet wave first studied by Tam & Hu (J. Fluid Mech., vol. 201, 1989, pp. 447-483). It is further demonstrated that screech tones are only observed over the frequency range where this upstream-travelling wave is propagative. [ABSTRACT FROM AUTHOR]

A fully three-dimensional linear stability analysis is carried out to investigate the unstable bifurcations of a compressible viscous fluid past a sphere. A time-stepper technique is used to compute both equilibrium states and leading eigenmodes. In agreement with previous studies, the numerical results reveal a regular bifurcation under the action of a steady mode and a supercritical Hopf bifurcation that causes the onset of unsteadiness but also illustrate the limitations of previous linear approaches, based on parallel and axisymmetric base flow assumptions, or weakly nonlinear theories. The evolution of the unstable bifurcations is investigated up to low-supersonic speeds. For increasing Mach numbers, the thresholds move towards higher Reynolds numbers. The unsteady fluctuations are weakened and an axisymmetrization of the base flow occurs. For a sufficiently high Reynolds number, the regular bifurcation disappears and the flow directly passes from an unsteady planar-symmetric solution to a stationary axisymmetric stable one when the Mach number is increased. A stability map is drawn by tracking the bifurcation boundaries for different Reynolds and Mach numbers. When supersonic conditions are reached, the flow becomes globally stable and switches to a noise-amplifier system. A continuous Gaussian white noise forcing is applied in front of the shock to examine the convective nature of the flow. A Fourier analysis and a dynamic mode decomposition show a modal response that recalls that of the incompressible unsteady cases. Although transition in the wake does not occur for the chosen Reynolds number and forcing amplitude, this suggests a link between subsonic and supersonic dynamics. [ABSTRACT FROM AUTHOR]

Steady self-similar solutions to the supersonic flow of Bethe--Zel'dovich--Thompson fluids past compressive and rarefactive ramps are derived. Inviscid, non-heatconducting, non-reacting and single-phase vapour flow is assumed. For convex isentropes and shock adiabats in the pressure--specific volume plane (classical gas dynamic regime), the well-known oblique shock and centred Prandtl--Meyer fan occur at a compressive and rarefactive ramp, respectively. For non-convex isentropes and shock adiabats (non-classical gas dynamic regime), four additional wave configurations may possibly occur; these are composite waves in which a Prandtl--Meyer fan is adjacent up to two oblique shock waves. The steady two-dimensional counterparts of the wave curves defined for the one-dimensional Riemann problem are constructed. In the present context, such curves consist of all the possible states connected to a given initial state (namely, the uniform state upstream of the ramp/wedge) by means of a steady self-similar solution. In addition to the classical case, as many as six non-classical wave-curve configurations are singled out. Moreover, the necessary conditions leading to each type of wave curves are analysed and a map of the upstream states leading to each configuration is determined. [ABSTRACT FROM AUTHOR]

This paper presents a robust, efficient, and strongly scalable solution methodology for simulation of complex turbulent flows on unstructured grids. The compressible Reynolds averaged Navier–Stokes (RANS) equations and the negative Spalart–Allmaras (SA) turbulence model are discretized, in coupled form, using a Streamline Upwind Petrov–Galerkin (SUPG) scheme. The time integration is fully implicit, and the discretized equations are advanced towards a steady-state solution using a pseudo-transient continuation (PTC). For solution of the linearized systems, a preconditioned Krylov solver is used. Seeking robustness, Krylov solvers are commonly preconditioned using incomplete factorization methods such as ILU(k). However, these methods are neither memory efficient, nor strongly scalable. To provide a better alternative, the implicit line solution method, which has been traditionally used in finite-volume methods, is revised and enhanced to solve stiffer linear systems. In the developed method, the lines are generated using a matrix-based approach, which connects the strongly-coupled unknowns. In addition, to improve the robustness of the line solver for high-CFL systems, a dual-CFL strategy, with a lower CFL number in the preconditioner matrix, is developed. Also, it is shown that for high-order continuous finite-element discretizations, the interconnections of the degrees of freedom on a line form a banded matrix which is wider than tridiagonal, but still can be factorized completely without generating any fill-ins. The developed line preconditioner is strongly scalable and, in contrast to the ILU factorization, its convergence behavior does not depend on the number of partitions. Two three-dimensional numerical examples are presented in which the performance of the line preconditioner is compared with that of the ILU(k) preconditioner. This comparison shows that, in addition to robustness improvements, the line preconditioner offers significant benefits in terms of memory efficiency. [ABSTRACT FROM AUTHOR]