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A new approach for solving steady incompressible Navier‐Stokes equations is presented in this paper. This method extends the upwind Riemann‐problem‐based techniques to viscous flows, which is obtained by applying modified artificial compressibility Navier‐Stokes equations and fully discrete high‐order numerical schemes for systems of advection‐diffusion equations. In this approach, utilizing the local Riemann solutions the steady incompressible viscous flows can be solved in a similar way to that of inviscid hyperbolic conservation laws. Numerical experiments on the driven cavity problem indicate that this approach can give satisfactory solutions.

A numerical analysis is given for the prediction of unsteady, two‐dimensional fluid flow induced by a heat and mass source in an initially closed cavity which is vented when the internal overpressure reaches a certain level. A modified ICE technique is used for solving the Navier–Stokes equations governing a compressible flow at a low Mach number and high temperature. Particular attention is focused on the treatment of the boundary conditions on the vent surface. This has been treated by an original procedure using the resolution of a Riemann problem. The configuration investigated may be viewed as a test problem which allows simulation of the ventilation and cooling of such cavities. The injection of hot gases is found to play a key role on the temperature field in the enclosure, whereas the vent seems to produce a distortion of the dynamic flow‐field only. When the injection of hot gases is stopped, the enclosure heat transfer is strongly influenced by the vent. A comparison with the results obtained when the radiative heat transfer between the walls of the enclosure is considered, indicate that radiation dominates the heat transfer in the enclosure and alters the flow patterns significantly.

Presents a numerical solution to the Riemann problem inside a porous material using a TVD‐ based computer code which was developed during the investigation of the head‐on collision of planar shock waves with rigid porous materials. The numerical solution revealed that although the compaction wave propagates with a constant velocity, the flow field induced by it is not self‐similar. Since such a problem cannot be set up in a conventional shock tube, the present study should be considered as a theoretical one.

The purpose of this paper is twofold. Firstly, to present a detailed account of the generalized Lagrangian formulation of Hui and Zhao, in which the stream function ζ and Lagrangian distance λ, are used as independent variables, and secondly to assess and compare the performance of various flux limiters in this formulation with their corresponding performance in the Eulerian formulation. The generalized Lagrangian formulation is obtained by a transformation from the cartesian co‐ordinates (x, y) to the Lagrangian co‐ordinates (λ, ζ). In this manner, the number of independent variables for steady, 3‐D flow is reduced from four to three, placing this formulation on the same footing as the Eulerian formulation even for steady flows (as opposed to the conventional Lagrangian formulation which apparently still requires four independent variables even for steady flows). The generalized Lagrangian formulation with the Godunov scheme (using flux limiters) appears to have distinct advantages over the corresponding Eulerian formulation, particularly with respect to accuracy. Furthermore, the method requires no grid generation.

A shock capturing scheme is presented for the equations of isentropic flow based on upwind differencing applied to a locally linearized set of Riemann problems. This includes the two‐dimensional shallow water equations using the familiar gas dynamics analogy. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency, leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver where the computational expense can be prohibitive. The scheme is applied to a two‐dimensional dam‐break problem and the approximate solution compares well with those given by other authors.

This paper aimed to study the simulation and describe the turbulent fluid flow through a symmetrical tube with a propeller disk set inside it. The Navier–Stokes equations with the model of turbulence (k-ω) are used to describe this problem in space and time.

The propeller disk is represented by the distribution of the vector of velocities along its radius. The main purpose is to describe the boundary conditions at the inlet, at the outlet and special compatible conditions for the simulation of the propeller disk on the both sides. A one-side modification of the Riemann problem is used for the boundary value conditions. Total pressure and total density values and the angle of attack equal to zero are to be used preferentially at the inlet, whereas pressure should be used at the outlet. At the back side of the propeller disk, it is advantageous to use total density and total pressure distributions coming from the distribution of axial velocities on the disk and the total state values at the inlet, with extra-added velocities of rotation. At the front side of the propeller disk, it is preferable to use the distribution of the flowing mass known from the state values computed on the disk.

This set of boundary conditions allows simulation of the air flow twisting behind the propeller/fan including increases in the corresponding pressure.

The advantage of this approach is the possibility to solve axial cuts of air ducts. Similarly, it is possible to solve air flow around the engine nacelle of the propeller aircraft. By this approach, it is possible to separate the design of the axial cut air duct from the propeller solution.

This approach has been used for new air duct designed on the operating conditions with Star-CCM+ solver.

The purpose of this paper is to provide an improved Mie-Grüneisen mixture model to simulate underwater explosion (UNDEX).

By using Mie-Grüneisen equations of state (EOS) to model explosive charge, liquid water and solid structure, the whole fluid field is considered as a multi-phases mixture under Mie-Grüneisen EOS. Then by introducing auxiliary variables in Eulerian model and using mass fraction to establish a diffusion balance, a new improved Mie-Grüneisen mixture model is presented here. For the new reconstructed mixture model, a second order MUSCL scheme with TVD limiter is employed to solve the multi-phase Riemann problem.

Numerical examples show that the results obtained by Mie-Grüneisen mixture model are quite closed to theoretical and empirical data. The model can be also used in 2-D fluid-structure problem of UNDEX effectively and it is proved that the deformation of structure can be clearly described by mass fraction.

The FVM model based on mass fraction can only describe the motion of compressible material under impact. Material failure or large deformation needs a modification about the EOS or implementations of other models (i.e. FEM model).

An improved non-oscillation Mie-Grüneisen mixture model, which based on mass fraction, is given in the present paper. The present Mie-Grüneisen mixture model provides a simplified and efficient way to simulate UNDEX. The feasibility of this model to simulate the detonation impacts on different mediums, including water and other metal mediums, is tested and verified here. Then the model is applied to the simulation of underwater contact explosion problem. In the simulation, deformation of structure under explosion loads, as well as second shock wave, are studied here.

An algorithm based on flux difference splitting is presented for the solution of two‐dimensional, steady, supercritical open channel flows. A transformation maps a non‐rectangular, physical domain into a rectangular one. The governing equations are then the shallow water equations, including terms of slope and friction, in a generalised coordinate system. A regular mesh on a rectangular computational domain can then be employed. The resulting scheme has good jump capturing properties and the advantage of using boundary/body‐fitted meshes. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

In computational fluid dynamics for two-phase reactive flow of interior ballistic, the conventional schemes (MacCormack method, etc.) are known to introduce unphysical oscillations in the region where the gradient is high. This paper aims to improve the ability to capture the complex shock wave during the interior ballistic cycle.

A two-phase flow model is established to describe the complex physical process based on a modified two-fluid theory. The solution of model is obtained including the following key methods: an approximate Riemann solver to construct upwind fluxes, the MUSCL extension to achieve high-order accuracy, a splitting approach to solve source terms, a self-adapting method to expand the computational domain for projectile motion and a control volume conservation method for the moving boundary.

The paper is devoted to applying a high-resolution numerical method to simulate a transient two-phase reactive flow with moving boundary in guns. Several verification tests demonstrate the accuracy and reliability of this approach. Simulation of two-phase reaction flow with a projectile motion in a large-caliber gun shows an excellent agreement between numerical simulation and experimental measurements.

This paper has implications for improving the ability to capture the complex physics phenomena of two-phase flow during interior ballistic cycle and predict the combustion details, such as the flame spreading, the formation of pressure waves and so on.

This approach is reliable as a prediction tool for the understanding of the physical phenomenon and can therefore be used as an assessment tool for future interior ballistics studies.

The purpose of this work is to present the implementation of weighted essentially non-oscillatory (WENO) wavelet methods for solving multiphase flow problems. The particular interest is gas–liquid two-phase mixture with velocity non-equilibrium. Numerical simulations are carried out on different scenarios of one-dimensional Riemann problems for gas–liquid flows. Results are validated and qualitatively compared with solutions provided by other standard numerical methods.

This paper extends the framework of WENO wavelet adaptive method to a fully hyperbolic two-phase flow model in a conservative form. The grid adaptivity in each time step is provided by the application of a thresholded interpolating wavelet transform. This facilitates the construction of a small yet effective sparse point representation of the solution. The method of Lax–Friedrich flux splitting is used to resolve the spatial operator in which the flux derivatives are approximated by the WENO scheme.

Hyperbolic models of two-phase flow in conservative form are efficiently solved, as shocks and rarefaction waves are precisely captured by the chosen methodology. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions. The results indicate that WENO wavelet methods are robust and sufficient to accurately simulate gas–liquid mixtures.

Resolution of two-phase flows is rarely studied using WENO wavelet methods. It is the first time such a study on the relative velocity is reported in two-phase flows using such methods.