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The purpose of this paper is to present a new hybrid Euler flux fonction for use in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems.

The proposed scheme, called AUFSRR can be devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach (Sun and Takayama, 2003; Ren, 2003). The upwind direction is determined by the velocity-difference vector and idea is to apply the AUFS solver in the direction normal to shocks to suppress carbuncle and the Roe solver across shear layers to avoid an excessive amount of dissipation. The resulting flux functions can be implemented in a very simple manner, in the form of the Roe solver with modified wave speeds, so that converting an existing AUFS flux code into the new fluxes is an extremely simple task.

The proposed flux functions require about 18 per cent more CPU time than the Roe flux. Accuracy, efficiency and other essential features of AUFSRR scheme are evaluated by analyzing shock propagation behaviours for both the steady and unsteady compressible flows. This is demonstrated by several test cases (1D and 2D) with standard finite-volume Euler code, by comparing results with existing methods.

The hybrid Euler flux function is used in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems.

The AUFSRR scheme is devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach.

A new finite volume (FV) method is proposed for the solution of convection‐diffusion equations defined on 2D convex domains of general shape. The domain is approximated by a polygonal region; a structured non‐uniform mesh is defined; the domain is partitioned in control volumes. The conservative form of the problem is solved by imposing the law to be verified on each control volume. The dependent variable is approximated to the second order by means of a quadratic profile. When, for the hyperbolic equation, discontinuities are present, or when the gradient of the solution is very high, a cubic profile is defined in such a way that it enjoys unidirectional monotonicity. Numerical results are given.

The purpose of this paper is to simulate flow inside differentially heated rotating cavity using two different formulations; one using Navier‐Stokes (NS) equations derived in non‐inertial (rotating) frame of reference and the other using NS equations in inertial frame of reference. Then to compare the results obtained from these formulations to find their merits and demerits.

The NS equations for both non‐inertial and inertial formulations are written in artificial compressibility form before discretizing them by a high resolution finite volume method. The dual time steeping approach of Jameson is used for time accuracy in both the formulations. Arbitrary Lagrangian Eulerian (ALE) approach is used for taking care of moving boundary problem arising in the inertial formulation. A newly developed HLLC‐AC Riemann solver for discretizing convective fluxes and central differencing for discretizing viscous fluxes are used in the finite volume approach. Results for both the formulations are first validated with test cases reported in literature. Then the results of the two formulations are compared among themselves.

Results of the non‐inertial formulation obtained by the proposed method are found to match well with those reported in literature. The results of both the formulations match well for low rotational speeds of the cavity. The discrepancies between the results of the two formulations progressively increase with the increase in rotational speed. Implicit treatment of the source term is found to reduce the discrepancies.

The present approach is useful for accurate prediction of flow feature and heat transfer characteristic in case of applications such as manufacturing of single wafer crystal for semiconductor and in numerous metallurgical processes.

The ALE formulation is used for the first time to simulate a differentially heated rotating cavity problem. The attempt to compare non‐inertial and inertial formulations is also reported for the first time. Implicit treatment of the source term leading to change in solution accuracy is one of the important findings of the present investigation.

The flux vector splitting (FVS) schemes are known for their higher resistance to shock instabilities and carbuncle phenomena in high-speed flow computations, which are generally accompanied by relatively large numerical diffusion. However, it is desirable to control the numerical diffusion of FVS schemes inside the boundary layer for improved accuracy in viscous flow computations. This study aims to develop a new methodology for controlling the numerical diffusion of FVS schemes for viscous flow computations with the help of a recently developed boundary layer sensor.

The governing equations are solved using a cell-centered finite volume approach and Euler time integration. The gradients in the viscous fluxes are evaluated by applying the Green’s theorem. For the inviscid fluxes, a new approach is introduced, where the original upwind formulation of an FVS scheme is first cast into an equivalent central discretization along with a numerical diffusion term. Subsequently, the numerical diffusion is scaled down by using a novel scaling function that operates based on a boundary layer sensor. The effectiveness of the approach is demonstrated by applying the same on van Leer’s FVS and AUSM schemes. The resulting schemes are named as Diffusion-Regulated van Leer’s FVS-Viscous (DRvLFV) and Diffusion-Regulated AUSM-Viscous (DRAUSMV) schemes.

The numerical tests show that the DRvLFV scheme shows significant improvement over its parent scheme in resolving the skin friction and wall heat flux profiles. The DRAUSMV scheme is also found marginally more accurate than its parent scheme. However, stability requirements limit the scaling down of only the numerical diffusion term corresponding to the acoustic part of the AUSM scheme.

To the best of the authors’ knowledge, this is the first successful attempt to regulate the numerical diffusion of FVS schemes inside boundary layers by applying a novel scaling function to their artificial viscosity forms. The new methodology can reduce the erroneous smearing of boundary layers by FVS schemes in high-speed flow applications.

This study aims to feature the application of the artificial compressibility method (ACM) for the numerical prediction of two-dimensional (2D) axisymmetric swirling flows.

The respective academic numerical solver, named IGal2D, is based on the axisymmetric Reynolds-averaged Navier–Stokes (RANS) equations, arranged in a pseudo-Cartesian form, enhanced by the addition of the circumferential momentum equation. Discretization of spatial derivative terms within the governing equations is performed via unstructured 2D grid layouts, with a node-centered finite-volume scheme. For the evaluation of inviscid fluxes, the upwind Roe’s approximate Riemann solver is applied, coupled with a higher-order accurate spatial reconstruction, whereas an element-based approach is used for the calculation of gradients required for the viscous ones. Time integration is succeeded through a second-order accurate four-stage Runge-Kutta method, adopting additionally a local time-stepping technique. Further acceleration, in terms of computational time, is achieved by using an agglomeration multigrid scheme, incorporating the full approximation scheme in a V-cycle process, within an efficient edge-based data structure.

A detailed validation of the proposed numerical methodology is performed by encountering both inviscid and viscous (laminar and turbulent) swirling flows with axial symmetry. IGal2D is compared against the commercial software ANSYS fluent – by using appropriate metrics and characteristic flow quantities – but also against experimental measurements, confirming the proposed methodology’s potential to predict such flows in terms of accuracy.

This study provides a robust methodology for the accurate prediction of swirling flows by combining the axisymmetric RANS equations with ACM. In addition, a detailed description of the convective flux Jacobian is provided, filling a respective gap in research literature.

This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using numerical benchmarks.

The work presents a detailed comparison with reference solutions published in the literature –when available– and numerical results computed using a commercial cell-centred finite volume software.

The FCFV scheme provides first-order accurate approximations of the viscous stress tensor and the heat flux, insensitively to cell distortion or stretching. The strategy demonstrates its efficiency in inviscid and viscous flows, for a wide range of Mach numbers, also in the incompressible limit. In purely inviscid flows, non-oscillatory approximations are obtained in the presence of shock waves. In the incompressible limit, accurate solutions are computed without pressure correction algorithms. The method shows its superior performance for viscous high Mach number flows, achieving physically admissible solutions without carbuncle effect and predictions of quantities of interest with errors below 5%.

The FCFV method accurately evaluates, for a wide range of compressible laminar flows, quantities of engineering interest, such as drag, lift and heat transfer coefficients, on unstructured meshes featuring distorted and highly stretched cells, with an aspect ratio up to ten thousand. The method is suitable to simulate industrial flows on complex geometries, relaxing the requirements on mesh quality introduced by existing finite volume solvers and alleviating the need for time-consuming manual procedures for mesh generation to be performed by specialised technicians.

High‐power chemical lasers operating in high repetitive rate show a decrease of the output energy laser beam. In such lasers, the characteristic time which depends on the laser output is short in comparison with those related to the flow. Consequently, shock waves, acoustic waves and thermal perturbations, induced by the strong electric energy deposition and remaining in the laser cavity between two pulses, may explain the decrease of output energy of the laser beam. For a better understanding of the flowfields, a numerical approach is carried out using flux corrected transport algorithms (FCT methods) associated with a Riemann solver on the computational domain boundaries. Under two‐dimensional assumptions, the inviscid flow in the convergent‐divergent laser cavity is computed to describe the creation and propagation of the wave system and the hot gas column in both single and multidischarge operating modes. Distortions of the contact surfaces are put into evidence through the study of flowfield instabilities. Finally, the limitations of the two‐dimensional modelization become apparent. The numerical resolution is extended to a 3D case in order to take into account the optical direction. This allows to study the influence of shock waves travelling between optics and being generated by a side effect developing at the electrodes. These waves have an effect of long duration on the flowfield and lead to a high residual perturbation level.

The purpose of this paper is to explore the characteristics of hypersonic flow past a blunt body.

The implicit finite volume schemes are derived from axisymmetric Navier–Stokes equations by means of AUSM+ and LU-SGS methods, and programmed in FORTRAN. Based on the verified result that a 2D axisymmetric chemical equilibrium flow has a good agreement with the literature, the characteristics of hypersonic flow past a sphere are simulated by using four different models which involve four factors, namely, viscous, inviscid, equilibrium and calorically perfect gas.

Compared with the calorically perfect gas under hypervelocity condition, the shock wave of the equilibrium gas is more close to the blunt body, gas density and pressure become bigger, but gas temperature is lower due to the effect of real gas. Viscous effects are not obvious in the calculations of the equilibrium gas or the calorically perfect gas. In a word, the model of equilibrium gas is more suitable for hypersonic flow and the calculation of viscous flow has a smaller error.

The computer codes are developed to simulate the characteristics of hypersonic flows, and this study will be helpful for the design of the thermal protection system in hypersonic vehicles.

This paper aims to provide a validation of a state‐of‐the‐art methodology for computing three‐dimensional transitional flows in turbomachinery.

The Reynolds‐averaged Navier‐Stokes equations for compressible flows are solved. Turbulence is modeled using an explicit algebraic stress model and k−ω turbulence closure. A numerical method has been developed, based on a cell‐centered finite volume approach with Roe's approximate Riemann solver and formally second‐order‐accurate MUSCL extrapolation. The method is validated versus two severe test cases, namely, the subsonic flow through a turbine cascade with separated‐flow transition; and the transonic flow through a compressor cascade with transitional boundary layers, shock‐induced separation and corner stall. For the first test case, the transition model of Mayle for separated flow has been employed, whereas, for the second one, the transition has been modeled employing the Abu‐Ghannam and Shaw correlation.

The comparison of numerical results with the experimental data available in the literature shows that, for such complex flow configurations, an improved numerical solution could be achieved by employing transition models. Unfortunately, the available models are case‐dependent, each of them being suitable for specific applications.

A state‐of‐the‐art numerical methodology has been developed and applied to compute very complex flows in turbomachinery. Through an original analysis of the results, the merits and limits of the considered approach have been assessed. The paper points up the fundamental role of transition modeling for turbomachinery flow simulations.

This paper aims to improve the reliability of numerical methods for predicting the transient heat transfers in combustion chambers heated internally by moving heat sources.

A two-phase fluid dynamic model was used to govern the non-uniformly distributed moving heat sources. A Riemann-problem-based numerical scheme was provided to update the fluid field and provide convective boundary conditions for the heat transfer. The heat conduction in the solids was investigated by using a thermo-mechanical coupled model to obtain a reliable expanding velocity of the heat sources. The coupling between the combustion and the heat transfer is realized based on user subroutines VDFLUX and VUAMP in the commercial software ABAQUS.

The capability of the numerical scheme in capturing discontinuities in initial conditions and source terms was validated by comparing the predicted results of commonly used verification cases with the corresponding analytical solutions. The coupled model and the numerical methods are capable of investigating heat transfer problems accompanied by extreme conditions such as transient effects, high-temperature and high-pressure working conditions.

The work provides a reliable numerical method to obtain boundary conditions for predicting the heat transfers in solids heated by expanding multiphase reactive flows.