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Nearly 20 years after the birth of general-purpose GPU computing, the HPC landscape is now dominated by GPUs. After years of undisputed dominance by NVIDIA, new players have entered the arena in a convincing manner, namely AMD and more recently Intel, whose devices currently power the first two clusters in the Top500 ranking. Unfortunately, code porting is still a major problem, even more due to the presence of different vendors, but at the same time the emergence of simplified standard paradigms suggests an encouraging prospect for developers. In this work, we provide a detailed OpenMP porting strategy of STREAmS, a community code for the compressible fluid dynamics. The proposed porting technique is based on the offload functionality of the OpenMP 5.x paradigm and in particular on a hybrid directives/APIs approach that fits seamlessly into the multi-backend software ecosystem of STREAmS. We further carry out a comprehensive performance analysis on the Intel® Data Center GPU Max 1550 (formerly called Ponte Vecchio or PVC). In addition, we analyze the performance of the code on two benchmark clusters powered by PVC, including the exascale Aurora cluster. The performance is evaluated at different levels of parallelism involved, i.e., the intrinsic parallelism of the PVC tile, the inter-tile parallelism within the GPU configuration, between the GPUs within the node and between the nodes within the cluster. The analysis shows that although the implementation complexity of the OpenMP porting is limited, it is necessary to follow some important guidelines to achieve satisfactory performance. The PVC GPU shows about 40% higher performance than the NVIDIA A100 or AMD MI250X GPUs, which, however, were released about 3 years earlier. Both intra-node and internode scalability show good results. Overall, the introduction of PVC into the GPU computing HPC landscape represents a positive step forward for the diversification and competitiveness of the sector. [ABSTRACT FROM AUTHOR]

We consider in an infinite horizontal layer the stationary motion of a viscous compressible fluid in a magnetic field subject to the gravitational force, where the Dirichlet boundary condition for the velocity and similar but non-homogeneous and large enough conditions for the magnetic field are assumed. Existence of a stationary solution in a neighborhood close to the equilibrium state is obtained in Sobolev spaces as limit of a sequence of fixed points of some suitable operators. [ABSTRACT FROM AUTHOR]

We develop and analyze in this paper a momentum convection operator for variable density flows, and apply it to obtain a finite volume scheme for the Euler equations. The mesh is composed of triangular and quadrangular cells, in the two-dimensional case, and of hexahedral, tetrahedral, prismatic and pyramidal cells in three space dimensions. The approximation is staggered: the scalar variables (pressure, density and internal energy) are associated with the cells while the velocity approximation is face-centred. The derivation of the momentum convection operator extends to pyramids and prisms an already proposed construction for the other above-mentioned cells. The resulting operator takes the form of a finite volume operator, but is obtained by an algebraic process using as input the mass fluxes through the primal faces appearing in the mass balance for the definition of the velocity fluxes, with the only guideline to satisfy a discrete local kinetic energy identity. Its consistency thus deserves to be studied, and we show that this process yields a consistent convection operator in the Lax-Wendroff sense. Numerical tests confirm the expected scheme convergence, with a first-order rate on a pure shock solution. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the study of equations of viscous compressible and heat-conducting full magnetohydrodynamic (MHD) steady flows in a horizontal layer under the gravitational force and a large temperature gradient across the layer. We assume as boundary conditions, periodic conditions in the horizontal directions, while in the vertical directions, slip-boundary is assumed for the velocity, vertical conditions for the magnetic field, and fixed temperature or fixed heat flux are prescribed for the temperature. The existence of stationary solution in a small neighborhood of a stationary profile close to hydrostatic state is obtained in Sobolev spaces as a fixed point of some nonlinear operator.

This paper is concerned with the study of equations of viscous compressible and heat-conducting full magnetohydrodynamic (MHD) steady flows in a horizontal layer under the gravitational force and a large temperature gradient across the layer. We assume as boundary conditions, periodic conditions in the horizontal directions, while in the vertical directions, slip-boundary is assumed for the velocity, vertical conditions for the magnetic field, and fixed temperature or fixed heat flux are prescribed for the temperature. The existence of stationary solution in a small neighborhood of a stationary profile close to hydrostatic state is obtained in Sobolev spaces as a fixed point of some nonlinear operator. [ABSTRACT FROM AUTHOR]

We propose in this article a discretization of the momentum convection operator for fluid flow simulations on quadrangular or generalized hexahedral meshes. The space discretization is performed by the low‐order nonconforming Rannacher–Turek finite element: the scalar unknowns are associated with the cells of the mesh while the velocities unknowns are associated with the edges or faces. The momentum convection operator is of finite volume type, and its expression is derived, as in MUSCL schemes, by a two‐step technique: (i)$$ (i) $$ computation of a tentative flux, here, with a centered approximation of the velocity, and (ii)$$ (ii) $$ limitation of this flux using monotonicity arguments. The limitation procedure is of algebraic type, in the sense that its does not invoke any slope reconstruction, and is independent from the geometry of the cells. The derived discrete convection operator applies both to constant or variable density flows and may thus be implemented in a scheme for incompressible or compressible flows. To achieve this goal, we derive a discrete analogue of the computation ui(∂t(ρui)+div(ρuiu)=12∂t(ρui2)+12div(ρui2u)$$ {u}_i\kern0.3em \Big({\partial}_t\left(\rho {u}_i\right)+\operatorname{div}\left(\rho {u}_i\boldsymbol{u}\right)=\frac{1}{2}{\partial}_t\left(\rho {u}_i^2\right)+\frac{1}{2}\operatorname{div}\left(\rho {u}_i^2\boldsymbol{u}\right) $$ (with u$$ \boldsymbol{u} $$ the velocity, ui$$ {u}_i $$ one of its component, ρ$$ \rho $$ the density, and assuming that the mass balance holds) and discuss two applications of this result: first, we obtain stability results for a semi‐implicit in time scheme for incompressible and barotropic compressible flows; second, we build a consistent, semi‐implicit in time scheme that is based on the discretization of the internal energy balance rather than the total energy. The performance of the proposed discrete convection operator is assessed by numerical tests on the incompressible Navier–Stokes equations, the barotropic and the full compressible Navier–Stokes equations and the compressible Euler equations. [ABSTRACT FROM AUTHOR]

Although the gas kinetic schemes (GKS) have emerged as one of the powerful tools for simulating compressible flows, they exhibit several shortcomings. Since the local solution of continuous Boltzmann equation with the Maxwellian distribution function is used to calculate the numerical fluxes at the cell interface, the flux expression in GKS is usually more complicated. In this paper, a high‐order simplified gas kinetic flux solver (GKFS) is presented for simulating two‐dimensional compressible flows. Circular function‐based GKFS (C‐GKFS), which simplifies the Maxwellian distribution function into the circular function, combined with an improved weighted essentially non‐oscillatory (WENO‐Z) scheme is applied to capture more details of the flow fields with fewer grids. As a result, a simple high‐order accurate C‐GKFS is obtained, which improves the computing efficiency and reduce its complexity to facilitate the practical application of engineering. A series of benchmark‐test problems are simulated and good agreement can be obtained compared with the references, which demonstrate that the high‐order C‐GKFS can achieve the desired accuracy. [ABSTRACT FROM AUTHOR]

This paper is focused on the approximation of the Euler equations of compressible fluid dynamics on a staggered mesh. With this aim, the flow parameters are described by the velocity, the density, and the internal energy. The thermodynamic quantities are described on the elements of the mesh, and thus the approximation is only in L2, while the kinematic quantities are globally continuous. The method is general in the sense that the thermodynamic and kinetic parameters are described by an arbitrary degree of polynomials. In practice, the difference between the degrees of the kinematic parameters and the thermodynamic ones is set to 1. The integration in time is done using the forward Euler method but can be extended straightforwardly to higher-order methods. In order to guarantee that the limit solution will be a weak solution of the problem, we introduce a general correction method in the spirit of the Lagrangian staggered method described in [R. Abgrall and S. Tokareva, SIAM J. Sci. Comput., 39 (2017), pp. A2345--A2364; R. Abgrall, K. Lipnikov, N. Morgan, and S. Tokareva, SIAM J. Sci. Comput., 2 (2020), pp. A343--A370; V. A. Dobrev, T. V. Kolev, and R. N. Rieben, SIAM J. Sci. Comput., 34 (2012), pp. B606--B641], and we prove a Lax--Wendroff theorem. The proof is valid for multidimensional versions of the scheme, even though most of the numerical illustrations in this work, on classical benchmark problems, are one-dimensional because we have easy access to the exact solution for comparison. We conclude by explaining that the method is general and can be used in different settings, for example, finite volume or discontinuous Galerkin method, not just the specific one presented in this paper. [ABSTRACT FROM AUTHOR]

The goal of this paper is to investigate the aerodynamic and aerothermodynamic behavior of the Schiaparelli capsule after the deployment of a supersonic disk-gap-band (DGB) parachute during its re-entry phase into the Martian atmosphere. The novelty of this work lies in the investigation by LES (large-eddy simulations) of the coupled interaction of the flow field generated behind the capsule and that in front of the flexible DGB parachute. These simulations are performed at an altitude of 10 km and a Mach number around 2, i.e., a regime in which large canopy-area oscillations are observed. LES results have shown a strong interaction between the bow shock, the recompression and expansion waves, high pressure, density and temperature gradients, heat flux towards the airstream and the body implying turbulence generation, ingestion, and amplification through the shock waves. Vortices released from the capsule at a frequency of about 52 Hz and 159 Hz, corresponding to Strouhal numbers of ~0.2 and 0.75, respectively, are the main factors responsible for the instabilities of the hypersonic re-entry capsule and the disk-gap-band parachute coupled system. The nonlinear turbulence flow field generated at the capsule back is amplified when passing the parachute bow shock, and this is responsible for the non-axisymmetric behavior around and behind the parachute that caused the uncontrolled capsule oscillations and the Schiaparelli mission failure. In fact, an LES of the parachute without the capsule, for the same conditions, show a completely axisymmetric field, varying in time, but axisymmetric. In order to avoid this turbulence amplification, dampening of the vortex shedding is critical. Different techniques have been already proposed for other applications. In the case of capsule re-entry, due to the high temperatures in front of the capsule behind the bow shock since air plasma is generated, damping of the vortex shedding could be achieved by means of magnetohydrodynamic (MHD) control. [ABSTRACT FROM AUTHOR]

In this paper, we present the development of a third-order density-based solver within the Open- FOAM framework, tailored for handling compressible flows. The solver incorporates implicit variational reconstruction on three-dimensional unstructured meshes, as well as a novel technology coupling reconstruction and time integration for both steady and unsteady simulations. To address the challenge of achieving high-order accuracy for curved geometries, we introduce a new approach for curved wall boundary reconstruction, specifically designed for situations where high-order mesh information is not readily available in OpenFOAM. Furthermore, we propose a simple WBAP limiter capable of capturing shocks without necessitating the whole-domain successive limiting procedure. Numerical tests were conducted to assess the solver's performance. The results reveal that our established solver exhibits higher accuracy in smooth flow simulations, while maintaining an excellent balance between accuracy and robustness for problems involving strong shocks and other complex flow structures. [ABSTRACT FROM AUTHOR]

The goal of the present article is to understand the impact of numerical schemes for the reconstruction of data at cell faces in finite-volume methods, and to assess their interaction with the quadrature rule used to compute the average over the cell volume. Here, third-, fifth- and seventh-order WENO-Z schemes are investigated. On a problem with a smooth solution, the theoretical order of convergence rate for each method is retrieved, and changing the order of the reconstruction at cell faces does not impact the results, whereas for a shock-driven problem all the methods collapse to first-order. Study of the decay of compressible homogeneous isotropic turbulence reveals that using a high-order quadrature rule to compute the average over a finite-volume cell does not improve the spectral accuracy and that all methods present a second-order convergence rate. However the choice of the numerical method to reconstruct data at cell faces is found to be critical to correctly capture turbulent spectra. In the context of simulations with finite-volume methods of practical flows encountered in engineering applications, it becomes apparent that an efficient strategy is to perform the average integration with a low-order quadrature rule on a fine mesh resolution, whereas high-order schemes should be used to reconstruct data at cell faces.

It is known in the literature that in the case of compressible fluids, higher values than the fluid temperature are displayed on temperature sensors, partly due to the accumulation point flow. Depending on the operating point, this can be several degrees Celsius. One possibility of consideration is the so-called recovery factor. There are various theoretical approaches and models that have been transferred on the basis of measurement on the flat plate. In some cases, the recovery factor is only defined as a function of the Prandtl number. A test bench has been developed that can be used to determine the recovery factor of cylindrical, quere-flowed temperature sensors. Up to Ma numbers of about 0.5, sensors with different diameters, and thus different Reynolds numbers, were measured and the recovery factors were calculated. There is a pronounced dependence on both the Ma number and the Re number and the recovery factor is not constant. An empirical equation based on the measurement results is given, with which the recovery factor can be determined as a function of the fluid, the Mach- and Reynolds-numbers and thus a more accurate calculation of the real fluid temperature is possible.

This work presents an experimental investigation focused on the analysis of aerodynamic properties between two interacting spheres in a supersonic rarefied flow. Atmospheric re-entries of space debris, whether natural or man-made, begin at altitude 120 km, and observations of historical re-entries have shown that fragmentation occurs between 90 and 50 km. The resulting fragments interact with each other, altering their own trajectories while traversing the different flow regimes between the free molecular and continuum regimes. This study focuses on the intermediate slip regime, where viscous effects of varying magnitude can influence the nature of the interactions of the shocks and modify them from the already known behaviour in the continuum regime. Specifically, this study examines how two spheres interact with each other upon re-entry into the atmosphere, focusing particularly on the six types of shock/shock interactions identified by Edney. The experiments were performed in the MARHy wind tunnel, in a steady Mach 4 laminar flow with static pressure 2.67 Pa. To highlight the differences between the six types of interferences, a variety of set-ups and devices were used: flow-field visualization, aerodynamic forces (through two diagnoses, aerodynamic balance and the swinging sphere technique) and wall pressure measurements. Results demonstrate the identification of differences according to the type of interference observed, showing in particular the viscous effect of rarefied flows by making a comparison with the continuum regime. [ABSTRACT FROM AUTHOR]

Fuel injection is one of the most crucial components for scramjet engines, a promising hypersonic airbreathing technology for economical and flexible space transportation systems. While surrogate modeling based on machine learning has been employed to replace computational simulations for performance evaluation in design optimization of such components, it can inherently predict performance parameters only as scalar quantities. This study investigates the capability of deep learning to predict the fuel injection flowfields, aiming to assist with data-driven approaches for data mining and optimization. Two-dimensional flowfields with sonic fuel injection into a Mach 3.8 crossflow have been trained using the multilayer perceptron. The resultant model has been found to be able to predict the flowfields instantaneously with reasonable accuracy. Local sensitivity analysis has been performed to examine the influence of the design variables on flow properties to gain insights into the effects of their variations on local flow phenomena. [ABSTRACT FROM AUTHOR]

The Cartesian cut-cell method evaluates wall-fluid interactions by using the fluxes through a wall. This wall treatment by the Cartesian cut-cell method is expected to overcome the mass and energy conservation problems of the immersed boundary method. A wall flux evaluation using the image point is proposed in this study to avoid volume center estimation. The Cartesian cut-cell method that uses the proposed wall flux evaluation is validated by the numerical simulations of supersonic flows past simple shapes. In the numerical simulations of the supersonic flow past a cylinder with an isothermal wall, the shorter displacement dIP of the image point from the wall provided a better estimation of the wall heat flux. Furthermore, the wall heat flux distributions and the amount of heat converged with grid refinement. In the numerical simulations of the supersonic flow past a wedge, the minimum grid resolution of the Cartesian cut-cell method for wall flux estimation was suggested. Furthermore, the results of the isothermal wall condition, the adiabatic wall condition, and the inviscid condition were compared.

With a growing interest in low Reynolds number compressible flows, compressibility effects on the secondary instabilities developing on the circular cylinder periodic wake are investigated. The unsteady and time-averaged two-dimensional flows are characterised for Reynolds numbers Re ∈ [200; 350] and Mach numbers up to M͂ = 0.5, revealing different flow structures which influence the characteristics of the secondary unstable modes. The two-dimensional time-periodic solution is used as the base state for a global linear stability analysis performed by means of Floquet theory coupled with a time-stepping finite-difference approach of the nonlinear operator. The influence of compressibility on mode A and mode B secondary instabilities which are responsible for the three-dimensionalisation of the two-dimensional periodic wake is analysed. A stabilising or a destabilising effect of compressibility is observed on mode A, depending on the Reynolds number and the spanwise wavelength of the mode, while mode B is stabilised by the increase of the Mach number. Compressibility is indeed found to decrease the mode kinetic energy production due to base flow shear conversion, which drives the growth of mode B. This results in a delay of the three-dimensionalisation process of the wake due to compressibility. [ABSTRACT FROM AUTHOR]

The deformation and breakup characteristics of liquid rocket propellant 2 (RP-2) droplets are experimentally investigated in a shock tube. The RP-2 droplets are subjected to a weak shock wave, a strong shock, and a detonation wave to deduce the impacts of high-speed and supersonic reacting flows on droplet deformation and breakup. High-speed shadowgraph and schlieren imaging techniques are employed to characterize droplet morphologies, deformation rates, and displacement of the droplet centroid. The results reveal that the transition from a shock wave to a detonation suppresses the deformation of the droplet and augments small-scale breakup. A shift in dominant breakup mechanisms is linked to a significant increase in the Weber number due to an increase in flow velocities and temperatures when transitioning to the detonation case. The experimental data are combined with a droplet stability analysis to predict the "child" (or fragments of the initial "parent" droplet) droplet sizes of each test condition. The child droplet size is shown to decrease as the flow regime transitions toward a detonation. An analytical mass stripping model was also used to determine that the total mass stripped from the parent droplet increased when approaching supersonic reacting conditions. The child droplet sizes and mass stripping rate will ultimately influence evaporation timescales and ignition in supersonic reacting flows, which is important for the development of detonation-based propulsion and power systems. [ABSTRACT FROM AUTHOR]

While Eulerian smoothed particle hydrodynamics (SPH) method has received increasing attention in scientific and industrial communities owing to its high spatial accuracy, it exhibits excessive numerical dissipation due to the fact that the flux is derived in particle pair pattern. In this paper, we adopt a one-dimensional weighted essentially non-oscillatory (WENO) reconstruction to reduce the numerical dissipation and improve the overall accuracy particularly in capturing the contact discontinuity. The underlying principle is to construct a 4-point stencil along the interacting line of each particle pair and then the WENO scheme is applied to reconstruct the initial states of the Riemann problem which determines the flow flux. A set of benchmark tests for both compressible and incompressible flows are studied to investigate the accuracy, robustness and versatility of the proposed Eulerian SPH method with the WENO reconstruction (ESPH-WENO). [ABSTRACT FROM AUTHOR]

In recent years, CFD has proven to be a very useful asset to help with predicting complex flows in a wide range of situations, including multiphase and gas-particle flows. On this track, numerical modelling of particle-laden flows in multistage turbomachinery has become an important step in helping to analyse the behaviour of a discrete phase in gas turbines. Furthermore, unsteady effects due, for example, to rotor–stator interaction may have an effect on trajectories and capture efficiencies of the discrete phase. Unfortunately, computational times for transient simulations can be exceedingly high, especially if a discrete-phase needs also to be simulated. For this reason, this work reports a new method for the efficient and accurate simulation of particle-laden flows in gas turbine engines components. The Harmonic Balance Method is exploited to gain orders of magnitude speedup exploiting the idea that once the flow field has been embedded in the spectral basis, it can be reconstructed at any desired time. In this way, not only can the computational time needed to reach convergence of the flow field be dramatically reduced, but there is also no need to keep simulating the flow field during particle tracking. On the contrary, the continuous phase field can be retrieved at any desired time through flow reconstruction. This technique is conceptually simple, but, to the authors' knowledge, has never been applied so far in particle-laden flow simulations and represents a novelty in the field. First, the implementation of the method is described, and details are given on how phase-lagged boundary conditions can be applied to flow and particles to further speed up the calculation. Then, some relevant case studies are presented to highlight the performance of the method. [ABSTRACT FROM AUTHOR]

In this study, we consider the Oseen structure of the linearization of a compressible fluid–structure interaction (FSI) system for which the interaction interface is under the effect of material derivative term. The flow linearization is taken with respect to an arbitrary, variable ambient vector field. This process produces extra "convective derivative" and "material derivative" terms, which render the coupled system highly nondissipative. We show first a new well‐posedness result for the full incorporation of both Oseen terms, which provides a uniformly bounded semigroup via dissipativity and perturbation arguments. In addition, we analyze the long time dynamics in the sense of asymptotic (strong) stability in an invariant subspace (one‐dimensional less) of the entire state space, where the continuous semigroup is uniformly bounded. For this, we appeal to the pointwise resolvent condition introduced in Chill and Tomilov [Stability of operator semigroups: ideas and results, perspectives in operator theory Banach center publications, 75 (2007), Institute of Mathematics Polish Academy of Sciences, Warszawa, 71–109], which avoids an immensely technical and challenging spectral analysis and provides a short and relatively easy‐to‐follow proof. [ABSTRACT FROM AUTHOR]

Direct numerical simulations of the evolution of turbulent spots in the boundary layer on a flat plate at a zero angle of attack at the freestream Mach number M∞ = 6 are carried out. The propagation of artificially excited localized three-dimensional vortical disturbances with different initial amplitudes, which, when propagating downstream, develop into turbulent spots, is considered. A direct numerical simulation is performed by solving the Navier–Stokes equations for three-dimensional compressible gas flows using the in-house solver that implements an implicit shock capturing numerical scheme. It is shown that the universal quasi-monotonic numerical scheme makes it possible to correctly estimate the main characteristics of turbulent spots: the transverse spreading angle and the velocities of the leading and trailing fronts. The agreement between the parameters of the obtained spots and the results of other authors is demonstrated. [ABSTRACT FROM AUTHOR]

Particle-laden gas flows occur in a wide variety of process technologies. It is therefore a common safety scenario to understand how many particles will escape in the event of a leak or emergency pressure relief. Therefore, a vessel filled with gas and homogeneously dispersed solid particles was considered. The aim was to derive a model to describe the discharge of arbitrary spherical particles. For this purpose, multiple numerical simulations were performed with ANSYS CFX©. A cylindrical vessel with a volume of 2 m³, a 25 mm opening and a length to diameter ratio of 2 was considered. The system was considered adiabatic, isentropic, compressible, and subcritical with an ideal gas. The velocity field was described with a one-way Euler-Lagrange method. The particle density, particle size, the gas in the vessel, as well as the initial temperature and pressure in the vessel were varied. Based on a dimensional analysis a model was developed to estimate the discharged mass of particles. This model achieves a small mean absolute deviation from the simulation data of −0.03%. The prediction model is thus able to correctly represent all variables varied without having to carry out single complex numerical simulations. The model is the first model to derive the discharge behaviour of particles from pressure vessels.

The goal of this paper is to investigate the aerodynamic and aerothermodynamic behavior of the Schiaparelli capsule after the deployment of a supersonic disk-gap-band (DGB) parachute during its re-entry phase into the Martian atmosphere. The novelty of this work lies in the investigation by LES (large-eddy simulations) of the coupled interaction of the flow field generated behind the capsule and that in front of the flexible DGB parachute. These simulations are performed at an altitude of 10 km and a Mach number around 2, i.e., a regime in which large canopy-area oscillations are observed. LES results have shown a strong interaction between the bow shock, the recompression and expansion waves, high pressure, density and temperature gradients, heat flux towards the airstream and the body implying turbulence generation, ingestion, and amplification through the shock waves. Vortices released from the capsule at a frequency of about 52 Hz and 159 Hz, corresponding to Strouhal numbers of ~0.2 and 0.75, respectively, are the main factors responsible for the instabilities of the hypersonic re-entry capsule and the disk-gap-band parachute coupled system. The nonlinear turbulence flow field generated at the capsule back is amplified when passing the parachute bow shock, and this is responsible for the non-axisymmetric behavior around and behind the parachute that caused the uncontrolled capsule oscillations and the Schiaparelli mission failure. In fact, an LES of the parachute without the capsule, for the same conditions, show a completely axisymmetric field, varying in time, but axisymmetric. In order to avoid this turbulence amplification, dampening of the vortex shedding is critical. Different techniques have been already proposed for other applications. In the case of capsule re-entry, due to the high temperatures in front of the capsule behind the bow shock since air plasma is generated, damping of the vortex shedding could be achieved by means of magnetohydrodynamic (MHD) control.

Flows in which the primary features of interest do not rely on high-frequency acoustic effects, but in which long-wavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with low-Mach-number methods would remove all acoustic wave propagation, while integrating the entire domain with the fully compressible equations can in some cases be prohibitively expensive due to the CFL time step constraint. For example, simulation of thermoacoustic instabilities might require fine resolution of the fluid/chemistry interaction but not require fine resolution of acoustic effects, yet one does not want to neglect the long-wavelength wave propagation and its interaction with the larger domain. The present paper introduces a new multi-level hybrid algorithm to address these types of phenomena. In this new approach, the fully compressible Euler equations are solved on the entire domain, potentially with local refinement, while their low-Mach-number counterparts are solved on subregions of the domain with higher spatial resolution. The finest of the compressible levels communicates inhomogeneous divergence constraints to the coarsest of the low-Mach-number levels, allowing the low-Mach-number levels to retain the long-wavelength acoustics. The performance of the hybrid method is shown for a series of test cases, including results from a simulation of the aeroacoustic propagation generated from a Kelvin–Helmholtz instability in low-Mach-number mixing layers. It is demonstrated that compared to a purely compressible approach, the hybrid method allows time-steps two orders of magnitude larger at the finest level, leading to an overall reduction of the computational time by a factor of 8.

Flows in which the primary features of interest do not rely on high-frequency acoustic effects, but in which long-wavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with low-Mach-number methods would remove all acoustic wave propagation, while integrating the entire domain with the fully compressible equations can in some cases be prohibitively expensive due to the CFL time step constraint. For example, simulation of thermoacoustic instabilities might require fine resolution of the fluid/chemistry interaction but not require fine resolution of acoustic effects, yet one does not want to neglect the long-wavelength wave propagation and its interaction with the larger domain. The present paper introduces a new multi-level hybrid algorithm to address these types of phenomena. In this new approach, the fully compressible Euler equations are solved on the entire domain, potentially with local refinement, while their low-Mach-number counterparts are solved on subregions of the domain with higher spatial resolution. The finest of the compressible levels communicates inhomogeneous divergence constraints to the coarsest of the low-Mach-number levels, allowing the low-Mach-number levels to retain the long-wavelength acoustics. The performance of the hybrid method is shown for a series of test cases, including results from a simulation of the aeroacoustic propagation generated from a Kelvin–Helmholtz instability in low-Mach-number mixing layers. It is demonstrated that compared to a purely compressible approach, the hybrid method allows time-steps two orders of magnitude larger at the finest level, leading to an overall reduction of the computational time by a factor of 8.

Compressible flow varies from ideal-gas behaviour at high pressures where molecular interactions become important. It is widely accepted that density is well described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and pressure, based on two parameters, $A$ and $B$, related to intermolecular attraction and repulsion, respectively. Assuming small variations from ideal-gas behaviour, a closed-form approximate solution is obtained that is valid over a wide range of conditions. An expansion in these molecular interaction parameters simplifies relations for flow variables, elucidating the role of molecular repulsion and attraction in variations from ideal-gas behaviour. Real-gas modifications in density, enthalpy and sound speed for a given pressure and temperature lead to variations in many basic compressible-flow configurations. Sometimes, the variations can be substantial in quantitative or qualitative terms. The new approach is applied to choked-nozzle flow, isentropic flow, nonlinear wave propagation and flow across a shock wave, all for a real gas. Modifications are obtained for allowable mass flow through a choked nozzle, nozzle thrust, sonic wave speed, Riemann invariants, Prandtl’s shock relation and the Rankine–Hugoniot relations. Forced acoustic oscillations can show substantial augmentation of pressure amplitudes when real-gas effects are taken into account. Shocks at higher temperatures and pressures can have larger pressure jumps with real-gas effects. Weak shocks decay to zero strength at sonic speed. The proposed framework can rely on any cubic equation of state and can be applied to multicomponent flows or to more complex flow configurations.

This paper concerns the mathematical justification of a macroscopic Baer–Nunziato PDE bifluid system with a physical relaxation term that is linked to the two viscosities and the two pressure laws of the two compressible phases of the fluid which may be different. This is achieved using an homogenization approach in a periodic framework from a mesoscopic PDE description of two immiscible compressible viscous fluids with interfaces and no mass transfer. Our result extends the work in Bresch D, Hillairet M. [Note on the derivation of multi-component flow systems. Proc Am Math Soc. 2015;143:3429–3443] by allowing to consider different pressure laws for each component introducing an order parameter. This paper is complementary to the recent work [Bresch D, Burtea C, Lagoutière F. Mathematical justification of a compressible bi-fluid system with different pressure laws: a semi-discrete approach and numerical illustrations. Submitted 2021] which focuses on a semi-discretized approach and numerical illustrations. These two papers correspond to the extended versions of the document arXiv:2012.06497. [ABSTRACT FROM AUTHOR]

In this study, an immersed boundary method developed for compressible viscous flows (Ramakrishnan, R., Girdhar, A., & Ghosh, S. (2016). Immersed Boundary Methods for Compressible Laminar Flows) is modified to improve their stability and robustness. The embedded object is represented as a set of line segments in two dimensions with their outward unit normal vectors specified. A forcing method that leverages the finite volume approach is used, wherein the solution at the cell interfaces that lie near the boundaries of the embedded solid is reconstructed to implicitly satisfy boundary conditions at the immersed surface. The proposed immersed boundary method is validated for transonic inviscid flow past a bump in a channel, supersonic flow past a circular cylinder, transonic viscous flow past a NACA0012 airfoil, and supersonic viscous flow past a circular cylinder. The results are compared with simulations from the literature using contours of flow properties, surface pressure, or Mach number plots and show good agreement.

In this paper, based on our previous optimal compact schemes with minimized dispersion and controllable dissipation (OC–WENO schemes) (Sun et al. in Sci China-Phys Mech Astron 57:971–982, 2014), a spatio-temporal optimized, hybird compact-WENO scheme with minimized dispersion and critical-adaptive dissipation is developed for solving compressible flows. Firstly, the spectral properties of the fourth-order OC–WENO scheme is researched within the spatio-temporal discrete framework. In conjunction with total dispersion error of the fully scheme, an integrated error function is designed to optimize the dispersion property. Secondly, the scale sensor leveraged to quantify the local scaled wavenumber is optimized in the wavenumber space to improve the accuracy of estimating. Moreover, a dispersion-dissipation condition, controlling the relative proportion of dispersion and dissipation errors, is developed for the fully discrete scheme. Thirdly, by exploiting the optimized scale sensor and the dispersion-dissipation condition, the critical-adaptive dissipation surface is constructed to achieve the adaptive dissipation property relating to the local characteristics of the flow fields and different Courant number. To have the shock-capturing capability, the proposed compact scheme is blended with fifth-order WENO scheme to form the MDADFC–WENO scheme. Finally, a set of benchmark test cases is employed to validate the good performance of the proposed scheme. [ABSTRACT FROM AUTHOR]

Most technological advancements in medicine, process and energy engineering, life and food science, mobility and environmental engineering involve mastering fluid mechanical effects. In particular, compressible flow physics including shockwaves and phase‐interface interactions exhibit multi‐scale phenomena spanning several orders of magnitude upwards from nanometer and nanosecond time scales. Clearly, detailed analysis of such effects is impossible by means of experimental techniques. On the contrary, numerical modeling and simulations allow to capture the aforementioned mechanisms and provide non‐invasive access to any quantity of interest. Yet, the complex fluid physics require powerful computational methods utilizing recent advancements for high‐order schemes. In this work, we provide an overview on latest high‐order low‐dissipation schemes using level sets to model discontinuous phase‐interface interactions. [ABSTRACT FROM AUTHOR]

We present a detailed derivation of the Reynolds equation and its corresponding energy equation for three-dimensional, steady, laminar, compressible flows of single-phase Navier-Stokes fluids in thrust bearings. These equations are shown to be valid over most of the dense and supercritical gas regime except for the vicinity of the thermodynamic critical point. It is shown that the primary thermodynamic function governing the lubrication flow of high-pressure gases is the effective bulk modulus defined as the ratio of the bulk modulus to the shear viscosity. Numerical solutions to our Reynolds equation are obtained using a finite difference scheme for both moderate and high-speed flows. Approximate solutions to our Reynolds equation for high-speed flows are also derived through a perturbation analysis. It is found that boundary layers form on three out of four edges of the thrust pad. At the inner and outer radii of the pad, the flow is governed by a nonlinear heat equation. As the main flow leaves the pad, the flow is governed by a nonlinear relaxation equation. These three boundary layer solutions are rendered consistent by the construction of boundary layer solutions in the corner regions. A composite solution is developed which provides a single approximation and has the same accuracy as the individual approximations in their respective regions of validity. [ABSTRACT FROM AUTHOR]