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The shock instability, notably the disastrous carbuncle phenomenon, has plagued many low-dissipation Godunov-type numerical schemes in calculations of high Mach flows. In the current work, two popular stability analysis tools and corresponding numerical experiments are used to investigate the root cause of shock instability of the low-dissipation Harten, Lax, and van Leer with contact (HLLC) scheme. The local linear stability analysis reveals that the HLLC flux could attenuate all perturbations in the streamwise direction but not perturbations of density and shear velocity in the transverse direction. Numerical results also indicate that the shock instability of the HLLC scheme is only related to the transverse flux. The viscosity terms of entropy wave and shear wave are introduced into the transverse flux, and the stability analysis shows that with the help of additional viscosities the shock instability of the HLLC scheme is cured. To preserve the capability of resolving contact discontinuities and shear waves, a pressure-based switching function is incorporated into the expressions of viscosity terms so that the additional viscosities are activated only when calculating the transverse flux in the shock layer. A series of numerical experiments give evidence of the robustness and accuracy of the proposed scheme, and the strategy adopted here can be easily applied to cure shock instabilities of other low-dissipation numerical schemes, e.g., the Roe scheme and the AUSM+ scheme. [ABSTRACT FROM AUTHOR]

High-order spectral element methods are becoming more established for solving problems in computational fluid dynamics. In this paper, we introduce new stabilization parameters for the solution of compressible Navier-Stokes equations in conjunction with high-order spectral element methods. We previously defined a new set of stabilization parameters for Euler equations in a high-order spectral/hp framework. In this paper, we examine the definition of these stabilization parameters in the context of solutions of full Navier-Stokes equations, and we report good agreement with previously published results in the literature. We establish spectral L2 convergence of errors for Kovasznay flow. We then validate the definition of the stabilization parameter for Couette flow, flat plate, and compression corner problems. In a later example, we solve the flow past a cylinder and benchmark results with previously published results obtained with low-order methods and other approaches in compressible flow computations. We further solve hypersonic flow past a wedge and supersonic flow past a Flight Investigation of Re-Entry program (FIRE) entry capsule. We explore the definition of the shock-capturing parameter d based on the YZß parameter. The introduced definitions are found to provide excellent results for the full Navier-Stokes equations. [ABSTRACT FROM AUTHOR]

Oblique detonation waves (ODWs) have been widely studied due to their application potential for airbreathing hypersonic propulsion. Moreover, various formation structures of wedge-induced oblique detonation waves have been revealed in recent numerical investigations. Given the inflow conditions, the wave configuration is dependent on the wedge angle. Hence, any wedge-angle change will induce a transient ODW evolution to transition from one configuration to another. In this study, the transient development created by instantaneously changing the wedge angle is investigated numerically, based on the unsteady two-dimensional Euler equations and one-step irreversible Arrhenius chemical kinetics. The evolution caused by the abrupt wedge-angle change from one smooth initiation structure to another, both with a curved oblique shock/detonation surface at high-Mach-number regime, is investigated. Two processes are analyzed; the first consists of the downstream transition of the ODW initiation region the by decreasing the angle, and the second is the upstream transition by increasing the angle. In the downstream transition, the overall structure moves globally and readjusts continuously, generating an intermediate kinklike initiation structure. In the upstream transition, a localized reaction region forms and induces a more complex process, mainly derived from the different responding speeds of the oblique shock and detonation waves. To avoid the generation of the new localized explosion region, which causes an abrupt change in the initiation position and potentially affects the ODWE's stability and performance, it is suggested to vary the wedge angle in incremental steps within a certain time interval. [ABSTRACT FROM AUTHOR]

A numerical model of the internal flow in a duct rotating about one end is described. One-dimensional Euler equations are solved inside the duct using a finite volume formulation in which the advective fluxes are calculated using the advection upwind splitting method. The model was developed as a fast design tool for helicopter rotor blades with internal spanwise flow. To this end, centrifugal as well as Coriolis effects, frictional losses, duct sweep, and time-dependent duct boundary conditions are modeled, and a spanwise flow control valve can be included. The model is used to explore the behavior of a 2-m-long duct with a circular cross section, rotating at tip speeds of up to 260 m/s. The effects of centrifugal pumping, duct friction, duct sweep, and a flow control valve on the spanwise pressure and velocity distribution, mass flow rate of air through the duct, and torque required to spin the duct are discussed. [ABSTRACT FROM AUTHOR]

This study explored inviscid supersonic corner flows induced by three-dimensional symmetrical intersecting compression wedges by introducing the spatial dimension reduction theoretical approach to transform the three-dimensional steady shock/shock interaction problem into a two-dimensional pseudosteady problem; this method allows not only wave configurations, which include regular reflection and Mach reflection, to be determined accurately, but also flowfield characteristics, which include density, temperature, pressure, and total pressure recovery coefficient near the regular reflection point (or in the vicinity of the Mach reflection triple point), as well as the location and the strength of the Mach stem. Theoretical results were compared to numerical simulation (performed by solving three-dimensional inviscid Euler equations with an non-oscillatory and non-free-parameters dissipative finite difference scheme) and analyzed thoroughly. The effects of inflow Mach number, sweep angle, and wedge angle on flowfield parameters and wave configurations were also considered. The influence of sweep angle is negligible, but the effects of Mach number and wedge angle are significant. [ABSTRACT FROM AUTHOR]

The numerical simulation of meso-, convective-, and microscale atmospheric flows requires the solution of the Euler or the Navier-Stokes equations. Nonhydrostatic weather prediction algorithms often solve the equations in terms of derived quantities such as Exner pressure and potential temperature (and are thus not conservative) and/or as perturbations to the hydrostatically balanced equilibrium state. This paper presents a well-balanced, conservative finite difference formulation for the Euler equations with a gravitational source term, where the governing equations are solved as conservation laws for mass, momentum, and energy. Preservation of the hydrostatic balance to machine precision by the discretized equations is essential because atmospheric phenomena are often small perturbations to this balance. The proposed algorithm uses the weighted essentially nonoscillatory and compact-reconstruction weighted essentially nonoscillatory schemes for spatial discretization that yields high-order accurate solutions for smooth flows and is essentially nonoscillatory across strong gradients; however, the well-balanced formulation may be used with other conservative finite difference methods. The performance of the algorithm is demonstrated on test problems as well as benchmark atmospheric flow problems, and the results are verified with those in the literature. [ABSTRACT FROM AUTHOR]

A set of compact disturbance equations is developed for high-accuracy and efficient aeroacoustic simulations. The compact disturbance equations in their complete form are an exact rearrangement of the Navier-Stokes equations, but incorporate various linear and nonlinear disturbance equations such as the linearized Euler equations and the linearized Navier-Stokes equations. Their attractive mathematical properties facilitate the implementations of the full compact disturbance equations and the reduced equations in essentially the same form as in existing computational fluid dynamics solvers with minor modifications. A high-resolution unsteady simulation in a reduced domain can be embedded inside a less-expensive Reynolds-averaged Navier-Stokes solution of flow in a larger, possibly very complex, configuration. This results in a hybrid Reynolds-averaged Navier-Stokes/large-eddy simulation method with reduced meshing difficulties and computational costs, but improved grid qualities and more accurate boundary treatments for complex configurations. Furthermore, a seamless switch can be made between the embedded governing equations. This enables a novel closely coupled computational fluid dynamics/computational aeroacoustics approach for complex aeroacoustic applications, where the full Navier-Stokes equations can be recovered in the source region to capture the turbulent noise sources and the linearized Euler equations can be applied to simulate the noise propagation and possible reflection more accurately and efficiently. These benefits are demonstrated with three benchmark tests and excellent results are obtained. [ABSTRACT FROM AUTHOR]

The two-dimensional linearized Euler equations in the time domain are computed to obtain the sound field in a channel with a rigid upper wall and an acoustic liner on the bottom wall in the presence of a shear flow. The liner is a simple mass-spring-damper system. The shear flow has a rather thin boundary layer, and the mesh has to be refined close to the walls. The objective is to assess whether an instability can be computed and whether a computed instability is physical. The computations are backed by a linear stability analysis of the flow that is performed by solving a matrix eigenvalue problem. By comparing the results of the simulations of the linearized Euler equations with the results of the stability analysis, it is found that the computed instabilities are physical and that their characteristics can be predicted. The effect of using selective filtering on the wave-number spectrum is also discussed. [ABSTRACT FROM AUTHOR]

A methodology is presented for performing numerical aerodynamic shape optimization based on the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations. An initial multiblock structured mesh is first fit with B-spline volumes that form the basis for a hybrid mesh movement scheme that is tightly integrated with the geometry parameterization based on B-spline surfaces. The RANS equations and the one-equation Spalart-Allmaras turbulence model are solved in a fully coupled manner using an efficient parallel Newton-Krylov algorithm with approximate-Schur preconditioning. Gradient evaluations are performed using the discrete-adjoint approach with analytical differentiation of the discrete flow and mesh movement equations. The overall methodology remains robust even in the presence of large shape changes. Several examples of lift-constrained drag minimization are provided, including a study of the common research model wing geometry, a wing-body-tail geometry with a prescribed spanwise load distribution, and a blended-wing-body configuration. An example is provided that demonstrates that a wing optimized based on the Euler equations exhibits substantially inferior performance when subsequently analyzed based on the RANS equations relative to a wing optimized based on the RANS equations. [ABSTRACT FROM AUTHOR]

Aerodynamic shape optimization of aircraft configurations often ignores stability considerations. To address this, a method for the computation of static, dynamic, and transient aircraft stability derivatives and their sensitivities for use in gradient-based optimization is introduced and evaluated. Computational fluid dynamics in the form of a three-dimensional structured-grid multiblock flow solver with both Euler and Reynolds-averaged Navier-Stokes equations is used. To compute the stability derivatives, a time-spectral formulation is used to compute an oscillating solution for the configuration of interest. From this oscillating solution, a series of linear regressions is performed to calculate the various stability derivatives. Because the solution is time dependent, it contains the information required to compute the transient, or "dot," derivatives for the configuration. An adjoint method is used to compute the gradients of the stability derivatives of interest, enabling gradient-based stability-constrained aerodynamic shape optimization with respect to a large number of design variables. The computed stability derivatives are verified for an airfoil and validated for a generic unmanned combat aerial vehicle. The stability-constrained optimization of a wing demonstrates the viability and usefulness of the method for aircraft design optimization. [ABSTRACT FROM AUTHOR]

An acoustic analogy is developed to predict the noise from jet flows. It contains two source models that independently predict the noise from turbulence and shock wave shear layer interactions. The acoustic analogy is based on the Euler equations and separates the sources from propagation. Propagation effects are taken into account by approximating the vector Green's function of the linearized Euler equations with the use of a locally parallel mean flow assumption. A statistical model of the two-point cross correlation of the velocity fluctuations is used to describe the turbulence. The acoustic analogy attempts to take into account the correct scaling of the sources for a wide range of nozzle pressures and temperature ratios. It does not make assumptions regarding fine- or large-scale turbulent noise sources, self- or shear noise, or convective amplification. The acoustic analogy is partially informed by three-dimensional steady Reynolds-averaged Navier-Stokes solutions that include the nozzle geometry. The predictions are compared with experiments of jets operating subsonically through supersonically and at unheated and heated temperatures. Predictions generally capture the scaling of both mixing noise and broadband shock-associated noise for the conditions examined, but some discrepancies remain, which are due to the accuracy of the steady Reynolds-averaged Navier-Stokes turbulence model closure, the equivalent sources, and the use of a simplified vector Green's function solver of the linearized Euler equations using a locally parallel mean flow. [ABSTRACT FROM AUTHOR]

An aeroelastic model is developed by using multivariable solid-shell elements. Geometrical nonlinearity and the elimination of corresponding locking phenomena are considered accurately in the modeling. Unsteady aerodynamic forces are addressed by solving Euler flow dynamic equations. The computational-structural-dynamics solver is loosely coupled to the computational-fluid-dynamics solver, and the full match of the computational structural dynamics and computational fluid dynamics interfaces is achieved by three-dimensional modeling. An interpolation method using finite-element shape functions is developed to transform forces from aerodynamic grids to structural grids. The aerodynamic mesh deformation is obtained by using radial basis functions combined with the transfinite interpolation method. The aeroelastic model is validated through the study of the flutter and the limit cycle oscillation of a cropped delta wing in transonic flow. Moreover, the establishment of the aeroelastic model using multivariable solid shell elements is compared with other modeling methods. Improved numerical results show that the multivariable finite-element method is an efficient and capable tool for simulating geometrical nonlinearity, and the developed three-dimensional data-exchange method also plays a key role in the nonlinear aeroelastic modeling. [ABSTRACT FROM AUTHOR]

Although time-domain solutions of the linearized Euler equations are well adapted to study the acoustic propagation in an outdoor environment, the modeling of sources in motion in time-domain solvers has not been investigated in the literature yet. This is done here by considering distributed volume sources. First, the influence of the spatial distribution of the source on the acoustic field is analyzed. Results obtained for a nonmoving source are summarized, and the example of a Gaussian spatial distribution is presented. The case of a harmonic volume source moving at a constant speed is then investigated in the geometrical far field. The directivity of a noncompact source is shown to be dramatically different from that of a point source. Numerical simulations are performed in a threedimensional geometry in free-field configurations, and waveforms of the acoustic pressure exhibit Doppler shift and convective amplification. Finally, simulations of a broadband moving source above an impedance ground surface are presented. For a rigid ground, strong destructive and constructive interferences are observed. The numerical solution is in a very good agreement with an analytical solution. For finite-impedance surfaces, interferences are smoothed, and the acoustic pressure strongly depends on the impedance model. A low-frequency contribution is observed close to the ground in accordance with the ground characteristics. [ABSTRACT FROM AUTHOR]

A novel domain decomposition technique is applied that couples nonlinear and linear Euler solvers to model acoustic scattering of waves in the vicinity of high-velocity gradients and large-amplitude waves to reduce numerical resources. The linear solver is applied in domains in which the wave amplitude is small and linearization is applicable, whereas the nonlinear solver is used in the vicinity of high wave amplitudes and stagnation points. Three numerical models are compared in this paper: 1) a linear Euler, 2) a nonlinear Euler, and 3) the domain decomposition technique. For all three models, the finite difference dispersion relation preserving scheme is applied to all spatial derivatives and the low-dissipation-dispersion Runge-Kutta scheme is applied for the temporal integration. A perfectly matched layer is applied at the edges of the computational domain to absorb outgoing waves and minimize reflections. To include complex bodies and geometries, an overset mesh is applied. After model validation, the technique is applied to the acoustic scattering of a pulse and a periodic source from a circular cylinder in flow. The results conclude that a thin zone around a complex body is sufficient to accurately account for nonlinear effects in the vicinity of stagnation points and that the domain decomposition technique accurately predicts both the unsteady field and integral unsteady forces about bluff bodies compared with full nonlinear simulations. The results suggest that there is a 40% reduction in computational time using the domain decomposition technique compared with full nonlinear calculations. [ABSTRACT FROM AUTHOR]

The article presents a green-gauss/weighted-least squares hybrid gradient reconstruction method that is applicable to wide-ranging grid types or geometries, inspite of the growing attention to more sophisticated, higher order methods. It describes the Euler equations, which is discretized for finite volume method (FVM) and applied to a polyhedral computational cell. The flow computation around two-dimenstional airfoils using hybrid mesh is discussed.

Large-scale three-dimensional aerodynamic shape optimization based on the compressible Euler equations is considered. Shape calculus is used to derive an exact surface formulation of the gradients, enabling the computation of shape gradient information for each surface mesh node without having to calculate further mesh sensitivities. Special attention is paid to the applicability to large-scale three dimensional problems like the optimization of an Onera M6 wing or a complete blended-wing-body aircraft. The actual optimization is conducted in a one-shot fashion, in which the tangential Laplace operator is used as a Hessian approximation, thereby also preserving the regularity of the shape. [ABSTRACT FROM AUTHOR]

Adjoint optimization methods have proven successful for the control of turbulence and boundary layers and in the design of airfoils and aircraft. In this paper, the adjoint equations are extended to the problem of controlling steady, inviscid, supersonic flow with volumetric source terms in the Euler equations, that is, mass, momentum, and energy addition. The adjoint solutions are shown to indicate both the optimal location for the source placement and cost gradient. In the particular case of drag reduction by energy deposition, the gradient is proportional to energy efficiency and becomes a key factor in optimization. The general form of the problem makes these results applicable to all forms of volumetric control with the goals of drag reduction, lift enhancement, and the generation of pitching moments. [ABSTRACT FROM AUTHOR]

Two mechanisms control sound generated by combustion in gas turbines: direct combustion noise in which acoustic waves generated by the flame propagate from the combustion chamber to the outlet through turbine stages, and indirect combustion noise (or entropy noise) in which entropy waves created by unsteady combustion generate noise as they are accelerated through the turbine stages. These mechanisms can be studied in laboratories by sending acoustic and entropy waves through a nozzle as done in the Entropy Wave Generator experiment. Previous studies have addressed the case where the nozzle is choked and have demonstrated that indirect noise was large compared to direct noise, suggesting that indirect noise only could be retained for gas turbine studies. In the present study, subsonic cases are analysed using, first, a full numerical resolution of the unsteady Euler equations; second, an analytical method based on the work of Marble and Candel in the low-frequency limit, and, finally, the one-dimensional linearized Euler equations in the frequency domain. Results show that direct noise cannot be neglected in these situations and will have to be included for real gas turbines where the flow remains mostly subsonic. [ABSTRACT FROM AUTHOR]

The article focuses on the benchmarking of a coupled immersed-boundary-finite-element solver for use with flow-induced deformation (FID) modeling. It mentions other FID modeling efforts that utilized arbitrary Lagrangian-Eulerian techniques with simulations performed on a body-conformal mesh modified through a suitable remeshing algorithm. It talks about the use of immersed boundary method for flow simulation with a fixed Cartesian grid used to solve governing equations for the flow domain.

In the recent past, adjoint methods have been successfully applied in error estimation of integral outputs (functionals) of the numerical solution of partial differential equations. The adjoint solution can also be used as a grid adaptation indicator, with the objective of optimally targeting and reducing the numerical error in the functional of interest below a prespecified threshold. In situations where we seek to quantify the effect of aleatory uncertainties on statistical moments of the output functional, it becomes necessary to evaluate the functional accurately at multiple sample points in probability space. If the numerical accuracy of these sample evaluations is not uniform, variations in the numerical error can affect the evaluation of the statistical moments. Although it is possible to independently adapt the meshes to obtain more accurate solutions at each sample point in stochastic space, such a procedure can be both cumbersome and computationally expensive. To improve the efficiency of this process, a new robust grid adaptation technique is proposed that is aimed at minimizing the numerical error over a range of variations of the uncertain parameters of interest about a nominal state. Using this approach, it is possible to generate computational grids that are insensitive to small variations of the uncertain parameters that can both locally and globally change the solution and, as a result, the error distribution. This is in contrast with classical adjoint techniques, which seek to adapt the grid with the aim of minimizing numerical errors for a specific flow condition (and geometry). It is demonstrated that flow computations on these robust grids result in low numerical errors under the expected range of variations of the uncertain input parameters. The effectiveness of this strategy is demonstrated in problems involving the Poisson equation and the Euler equations at transonic and supersonic!hypersonic speeds. [ABSTRACT FROM AUTHOR]

A Newton-Krylov algorithm for aerodynamic shape optimization in three dimensions is presented for both single-point and multipoint optimization. An inexact Newton method is used to solve the Euler equations, a discrete adjoint method is used to compute the gradient, and an optimizer based on a quasi-Newton method is used to find the optimal geometry. The flexible generalized minimal residual method is used with approximate Schur preconditioning to solve both the flow equation and the adjoint equation. The wing geometry is parameterized by B-spline surfaces, and a fast algebraic algorithm is used for grid movement at each iteration. An effective strategy is presented to enable simultaneous optimization of planform variables and section shapes. Optimization results are presented with up to 225 design variables to demonstrate the capabilities and efficiency of the approach. [ABSTRACT FROM AUTHOR]