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Article

Ghislain Tchuen, Pascalin Tiam Kapen and Yves Burtschell

– 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.

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Practical implications

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

Originality/value

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

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Thomas Rowan and Mohammed Seaid

The purpose of this paper is to present a new numerical model for shallow water flows over heterogeneous sedimentary layers. It is already several years since the…

Abstract

Purpose

The purpose of this paper is to present a new numerical model for shallow water flows over heterogeneous sedimentary layers. It is already several years since the single-layered models have been used to model shallow water flows over erodible beds. Although such models present a real opportunity for shallow water flows over movable beds, this paper is the first to propose a multilayered solver for this class of flow problems.

Design/methodology/approach

Multilayered beds formed with different erodible soils are considered in this study. The governing equations consist of the well-established shallow water equations for the flow, a transport equation for the suspended sediments, an Exner-type equation for the bed load and a set of empirical equations for erosion and deposition terms. For the numerical solution of the coupled system, the authors consider a non-homogeneous Riemann solver equipped with interface-tracking tools to resolve discontinuous soil properties in the multilayered bed. The solver consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms.

Findings

This paper reveals that modeling shallow water flows over multilayered sedimentary topography can be achieved by using a coupled system of partial differential equations governing sediment transport. The obtained results demonstrate that the proposed numerical model preserves the conservation property, and it provides accurate results, avoiding numerical oscillations and numerical dissipation in the approximated solutions.

Originality/value

A novel implementation of sediment handling is presented where both averaged and separate values for sediment species are used to ensure speed and precision in the simulations.

Details

Engineering Computations, vol. 37 no. 2
Type: Research Article
ISSN: 0264-4401

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Article

P. Glaister

A shock capturing scheme is presented for the equations of isentropicflow based on upwind differencing applied to a locally linearized set ofRiemann problems. This…

Abstract

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 4 no. 5
Type: Research Article
ISSN: 0961-5539

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Article

C.P.T. GROTH and J.J. GOTTLIEB

Partially‐decoupled upwind‐based total‐variation‐diminishing (TVD) finite‐difference schemes for the solution of the conservation laws governing two‐dimensional…

Abstract

Partially‐decoupled upwind‐based total‐variation‐diminishing (TVD) finite‐difference schemes for the solution of the conservation laws governing two‐dimensional non‐equilibrium vibrationally relaxing and chemically reacting flows of thermally‐perfect gaseous mixtures are presented. In these methods, a novel partially‐decoupled flux‐difference splitting approach is adopted. The fluid conservation laws and species concentration and vibrational energy equations are decoupled by means of a frozen flow approximation. The resulting partially‐decoupled gas‐dynamic and thermodynamic subsystems are then solved alternately in a lagged manner within a time marching procedure, thereby providing explicit coupling between the two equation sets. Both time‐split semi‐implicit and factored implicit flux‐limited TVD upwind schemes are described. The semi‐implicit formulation is more appropriate for unsteady applications whereas the factored implicit form is useful for obtaining steady‐state solutions. Extensions of Roe's approximate Riemann solvers, giving the eigenvalues and eigenvectors of the fully coupled systems, are used to evaluate the numerical flux functions. Additional modifications to the Riemann solutions are also described which ensure that the approximate solutions are not aphysical. The proposed partially‐decoupled methods are shown to have several computational advantages over chemistry‐split and fully coupled techniques. Furthermore, numerical results for single, complex, and double Mach reflection flows, as well as corner‐expansion and blunt‐body flows, using a five‐species four‐temperature model for air demonstrate the capabilities of the methods.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 3 no. 6
Type: Research Article
ISSN: 0961-5539

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Article

Cheng Cheng and Xiaobing Zhang

In computational fluid dynamics for two-phase reactive flow of interior ballistic, the conventional schemes (MacCormack method, etc.) are known to introduce unphysical…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Practical implications

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.

Originality/value

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Konstantinos Stokos, Socrates Vrahliotis, Theodora Pappou and Sokrates Tsangaris

– The purpose of this paper is to present a numerical method for the simulation of steady and unsteady incompressible laminar flows, including convective heat transfer.

Abstract

Purpose

The purpose of this paper is to present a numerical method for the simulation of steady and unsteady incompressible laminar flows, including convective heat transfer.

Design/methodology/approach

A node centered, finite volume discretization technique is applied on hybrid meshes. The developed solver, is based on the artificial compressibility approach.

Findings

A sufficient number of representative test cases have been examined for the validation of this numerical solver. A wide range of the various dimensionless parameters were applied for different working fluids, in order to estimate the general applicability of our solver. The obtained results agree well with those published by other researchers. The strongly coupled solution of the governing equations showed superiority compared to the loosely coupled solution as inviscid effects increase.

Practical implications

Convective heat transfer is dominant in a wide variety of practical engineering problems, such as cooling of electronic chips, design of heat exchangers and fire simulation and suspension in tunnels.

Originality/value

A comparison between the strongly coupled solution and the loosely coupled solution of the Navier-Stokes and energy equations is presented. A robust upwind scheme based on Roe’s approximate Riemann solver is proposed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

J. SHI and E.F. TORO

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…

Abstract

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

S. SOLTANI, K. MORGAN and J. PERAIRE

An upwind unstructured grid cell‐centred scheme for the solution of the compressible Euler and Navier‐Stokes equations in two dimensions is presented. The algorithm…

Abstract

An upwind unstructured grid cell‐centred scheme for the solution of the compressible Euler and Navier‐Stokes equations in two dimensions is presented. The algorithm employs a finite volume formulation. Calculation of the inviscid fluxes is based on the approximate Riemann solver of Roe. Viscous fluxes are obtained from solution gradients computed by a variational recovery procedure. Higher order accuracy is achieved through performing a monotonic linear reconstruction of the solution over each cell. The steady state is obtained by a point implicit time integration of the unsteady equations using local time stepping. For supersonic inviscid flow an alternative space marching algorithm is proposed. This latter approach is applicable to supersonic flow fields containing regions of local subsonic flow. Numerical results are presented to show the performance of the proposed scheme for inviscid and viscous flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 3 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Eric Daniel and Jean‐Claude Loraud

A numerical simulation of a two‐phase dilute flow (droplet‐gas mixture) is carried out by using a finite volume method based on Riemann solvers. The computational domain…

Abstract

A numerical simulation of a two‐phase dilute flow (droplet‐gas mixture) is carried out by using a finite volume method based on Riemann solvers. The computational domain represents a one‐ended pipe with holes at its upper wall which lead into an enclosure. The aim of this study is to determine the parameters of such a flow. More specially, an analytical solution is compared with numerical results to assess the mass flow rates through the vents in the pipe. Inertia effects dominate the dynamic behaviour of droplets, which causes a non‐homogeneous flow in the cavity. The unsteady effects are also important, which makes isentropical calculation irrelevant and shows the necessity of the use of CFD tools to predict such flows. No relation can be extracted from the numerical results between the gas and the dispersed mass flow rates across the holes. But a linear variation law for the droplet mass flow versus the position of the holes is pointed out, which is independent of the incoming flow when the evaporating effects are quite low.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 8 no. 2
Type: Research Article
ISSN: 0961-5539

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Article

Zhijian Duan and Gongnan Xie

The discontinuous Galerkin finite element method (DGFEM) is very suited for realizing high order resolution approximations on unstructured grids for calculating the…

Abstract

Purpose

The discontinuous Galerkin finite element method (DGFEM) is very suited for realizing high order resolution approximations on unstructured grids for calculating the hyperbolic conservation law. However, it requires a significant amount of computing resources. Therefore, this paper aims to investigate how to solve the Euler equations in parallel systems and improve the parallel performance.

Design/methodology/approach

Discontinuous Galerkin discretization is used for the compressible inviscid Euler equations. The multi-level domain decomposition strategy was used to deal with the computational grids and ensure the calculation load balancing. The total variation diminishing (TVD) Runge–Kutta (RK) scheme coupled with the multigrid strategy was employed to further improve parallel efficiency. Moreover, the Newton Block Gauss–Seidel (GS) method was adopted to accelerate convergence and improve the iteration efficiency.

Findings

Numerical experiments were implemented for the compressible inviscid flow problems around NACA0012 airfoil, over M6 wing and DLR-F6 configuration. The parallel acceleration is near to a linear convergence. The results indicate that the present parallel algorithm can reduce computational time significantly and allocate memory reasonably, which has high parallel efficiency and speedup, and it is well-suited to large-scale scientific computational problems on multiple instruction stream multiple data stream model.

Originality/value

The parallel DGFEM coupled with TVD RK and the Newton Block GS methods was presented for hyperbolic conservation law on unstructured meshes.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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