Compact upwind algorithms for viscous compressible flow calculations

A family of high-order accurate compact upwind difference operators have been used together with the split fluxes of the KFVS (Kinetic Flux Vector Splitting) scheme to obtain high order semi-discretizations of nonlinear convective terms in 2-D Navier-Stokes equations governing viscous compressible flows. A TVD multi-stage Runge-Kutta time stepping scheme is used to compute steady states for selected transonic/supersonic inviscid and viscous flow problems which indicate the higher accuracy and low diffusion realizable in such schemes. This work was done as part of the Indo-Russian Long-Term integrated programme and was supported by the Department of Science & Technology, Government of India.     

Evaluation of non-oscillatory schemes based on LED principle for supersonic flow computations

Summary The objective of the present paper is to evaluate the efficiency of several high resolution, non-oscillatory schemes based on the local extremum diminishing (LED) principle [1], [2] in the case of supersonic flow computation past obstacles in two dimensions. The Euler equations of gas dynamics have been solved in a cell-vertex finite volume framework in conjunction with the non-oscillatory dissipation schemes for simulation of supersonic flow fields. Satisfactory results have been obtained with the switched as well as the flux limited dissipation schemes, namely, SLIP and USLIP schemes using scalar diffusive flux. Four different types of flux splitting techniques have also been investigated along with the switched scheme. In particular, the wave-particle splitting proposed by Balakrishnan and Deshpande [3] for upwind schemes has been formulated and applied to the present symmetric or central scheme.     

Boltzmann schemes for continuum gas dynamics

Many problems arising in the aerodynamic design of aerospace vehicles require the numerical solution of the Euler equations of gas dynamics. These are nonlinear partial differential equations admitting weak solutions such as shock waves and constructing robust numerical schemes for these equations is a challenging task. A new line of research called Boltzmann or kinetic schemes discussed in the present paper exploits the connection between the Boltzmann equation of the kinetic theory of gases and the Euler equations for inviscid compressible flows. Because of this connection, a suitable moment of a numerical scheme for the Boltzmann equation yields a numerical scheme for the Euler equations. This idea called the “moment method strategy” turns out to be an extremely rich methodology for developing robust numerical schemes for the Euler equations. The richness is demonstrated by developing a variety of kinetic schemes such as kinetic numerical method, kinetic flux vector splitting method, thermal velocity based splitting, multidirectional upwind method and least squares weak upwind scheme. A 3-D time-marching Euler code calledbheema based on the kinetic flux vector splitting method and its variants involving equilibrium chemistry have been developed for computing hypersonic reentry flows. The results obtained from the codebheema demonstrate the robustness and the utility of the kinetic flux vector splitting method as a design tool in aerodynamics. The work presented in this paper is based on the research work done by several graduate students at our laboratory and collaborators from research and development organizations within the country.     

Simulation of hypersonic flows on unstructured grids

The paper describes a solver for the compressible inviscid flow equations which is based on a flux vector splitting strategy able to deal with chemical reaction effects. The methodology here adopted is based on a modification of the Flux Vector Splitting technique due to van Leer.¹¹ The scheme operates on completely unstructured grids and has been coupled with an adaptive remeshing procedure to compute high speed flows. Solutions for two-dimensional problems for non-reactive and reactive air in thermodynamic equilibrium are presented.     

Application of dynamic recursive splitting to estimate fibre entanglement in simulated nonwoven fibrous assemblies

Fibrous nonwovens comprise of fibres or filaments bonded by various methods. Depending on the mode of fabric formation these fibres may be entangled; this affects the physical properties of the bulk structure. Estimating the degree of entanglement based on relative fibre arrangement in such structures is highly challenging. In this paper, fibre-to-fibre interactions within simulated fibrous assemblies are analysed using topological and geometrical principles as a means to quantify entanglement. The underlying theoretical framework in which splitting number is used to characterise entanglement has been previously described [1]. A detailed algorithm and its practical application for the estimation of fibre entanglement are reported based on Dynamic Recursive Splitting (DYRES).     

拦截导弹热保护罩分离对红外窗口影响研究

高层防空拦截弹热保护罩的分离对红外窗口产生了巨大影响,该文采用可压雷诺平均Navier-Stokes方程、多块嵌套结构动网格技术和有限体积法模拟了热保护罩分离。采用FDS-ROE格式对Navier-Stokes方程进行离散,并通过LUSGS方法构造了二阶隐式的双时间推进格式。从而给出了分离过程中,由于激波干扰引起的红外...     

高超声速稀薄流场AUSM分裂式DSMC-IP方法研究

针对直接模拟蒙特卡洛(DSMC)方法统计耗散较大而传统的信息保存(DSMC-IP)方法难以有效模拟强激波的问题,采用对流迎风分裂(AUSM)通量计算格式对IP方法进行改造.以局部马赫数为标准重构控制方程中的关联项通量,使计算更加准确的符合激波两侧的流动特征,从而形成一种具有较高统计精度和高超声速流动模拟能力的新型DSM...     

Meshless techniques for convection dominated problems

In this paper, the stability problem in the analysis of the convection dominated problems using meshfree methods is first discussed through an example problem of steady state convection-diffusion. Several techniques are then developed to overcome the instability issues in convection dominated phenomenon simulated using meshfree collocation methods. These techniques include: the enlargement of the local support domain, the upwind support domain, the adaptive upwind support domain, the biased support domain, the nodal refinement, and the adaptive analysis. These techniques are then demonstrated in one- and two-dimensional problems. Numerical results for example problems demonstrate the techniques developed in this paper are effective to solve convection dominated problems, and in these techniques, using adaptive local support domain is the most effective method. Comparing with the conventional finite difference method (FDM) and the finite element method (FEM), the meshfree method has found some attractive advantages in solving the convection dominated problems, because it easily overcomes the instability issues.     

Design of single-polarization wavelength splitter based on photonic crystal fiber

A new single-polarization wavelength splitter based on the photonic crystal fiber (PCF) has been proposed. The full-vector finite-element method (FEM) is applied to analyze the single-polarization single-mode guiding properties. Splitting of two different wavelengths is realized by adjusting the structural parameters. The semi-vector three-dimensional beam propagation method is employed to confirm the wavelength splitting characteristics of the PCF. Numerical simulations show that the wavelengths of 1.3 μm and 1.55 μm are split for a fiber length of 10.7 mm with single-polarization guiding in each core. The crosstalk between the two cores is low over appreciable optical bandwidths.     

On the treatment of time-dependent boundary conditions in splitting methods for parabolic differential equations

Splitting methods for time-dependent partial differential equations usually exhibit a drop in accuracy if boundary conditions become time-dependent. This phenomenon is investigated for a class of splitting methods for two-space dimensional parabolic partial differential equations. A boundary-value correction discussed in a paper by Fairweather and Mitchell for the Laplace equation with Dirichlet conditions, is generalized for a wide class of initial boundary-value problems. A numerical comparison is made for the ADI method of Peaceman-Rachford and the LOD method of Yanenko applied to problems with Dirichlet boundary conditions and non-Dirichlet boundary conditions.     

Splitting tensile test for fibre reinforced concrete

The splitting tensile test is a much used method to determine the tensile strength of concrete. The conventional test procedure is known to have a number of limitations related to size effect and boundary conditions. Furthermore, it has been reported to be impossible to determine the tensile strength of Fibre Reinforced Concrete (FRC) using the standard splitting tensile test method. The objective of this paper is to present a methodology to obtain a close estimate of the true tensile strength of FRC from an adjusted tensile splitting test procedure. Splitting tests were performed on cylindrical specimens of four FRC mixes. The transversal deformation perpendicular to the load direction was recorded during the tests. The experimental load-deformation curves thus obtained have two peaks, an initial one as a result of the tensile stresses at the centre of the specimen and a second peak due to secondary cracking outside the loading axis. The tensile strength can be calculated from the first peak which represents the elastic limit state for the material. The method is validated through numerical simulation of the splitting tests using a cohesive crack approach. It is concluded that it is possible to obtain a close estimate of the true tensile strength of FRC using the procedure developed in the paper.     

A partial upwind finite element approximation for the stationary Navier-Stokes equations

A new partial upwind finite element method for steady viscous incompressible flow over a wide range of Reynolds numbers (Re) is proposed and its applications to a cavity flow problem are demonstrated. Numerical experiments show that the partial upwind scheme is effective for Re = 10³ when the conventional Galerkin type approximation produces poor results. The partial upwind scheme for the finite element method was originally developed by Ikeda (1983) for approximation of the advection diffusion equation. The advantage of the scheme is its effectiveness over a wide range of Peclet numbers due to the automatic switch in the approximation techniques of the advection term.     

Werkstoff und Mechanik beim Bruchtrennen von Automobil‐Pleueln

Materials and Mechanics for Fracture Splitting of Automobile Connecting Rods The technology of fracture splitting is used in the series production of connecting rods for automobile engines for cost savings. The loading mechanics, process related and material specific conditions for good splitting results are described on the basis of literature and our own observations. Conclusions are drawn concerning the avoidance of occasional fabrication defects and a transfer of the technology to new usage cases.     

An analysis of the convection-diffusion problems using meshless and meshbased methods

The numerical solution of the convection-diffusion equation represents a very important issue in many numerical methods that need some artificial methods to obtain stable and accurate solutions. In this article, a meshless method based on the local Petrov-Galerkin method is applied to solve this equation. The essential boundary condition is enforced by the transformation method, and the MLS method is used for the interpolation schemes. The streamline upwind Petrov-Galerkin (SUPG) scheme is developed to employ on the present meshless method to overcome the influence of false diffusion. In order to validate the stability and accuracy of the present method, the model is used to solve two different cases and the results of the present method are compared with the results of the upwind scheme of the MLPG method and the high order upwind scheme (QUICK) of the finite volume method. The computational results show that fairly accurate solutions can be obtained for high Peclet number and the SUPG scheme can very well eliminate the influence of false diffusion.     

An improved localized radial basis function meshless method for computational aeroacoustics

An improved localized radial basis function collocation method is developed for computational aeroacoustics, which is based on an improved localized RBF expansion using Hardy multiquadrics for the desired unknowns. The method approximates the spatial derivatives by RBF interpolation using a small set of nodes in the neighborhood of any data center. This approach yields the generation of a small interpolation matrix for each data center and hence advancing solutions in time will be of comparatively lower cost. An upwind implementation is further introduced to contain the hyperbolic property of the governing equations by using flux vector splitting method. The 4–6 low dispersion and low dissipation Runge–Kutta optimized scheme is used for temporal integration. Corresponding boundary conditions are enforced exactly at a discrete set of boundary nodes. The performances of the present method are demonstrated through their application to a variety of benchmark problems and are compared with the exact solutions.     

The numerical solution of two-dimensional,steady flow problems by the finite element method

Finite element equivalents of the equations governing shearing and buoyancy driven flows are derived, and reduced to upwind forms suitable for the solution of problems in which the Reynolds and Rayleigh numbers are large. A modification to the central difference iterative method is studied which increases the Reynolds and Rayleigh numbers for which a central difference form may be used. A comparison is made between the results obtained using the central and upwind forms of the finite element method and those predicted by finite difference methods in the case of flow in a cavity. A mesh refinement study is made. The upwind forms of the finite element equations are applied to the solution of a complex flow problem involving the flow of glass in a throated furnace in the case of constant- and temperature- dependent viscosity and conductivity.     

Oscillation limits for weighted residual methods applied to convective diffusion equations

Convection–diffusion equations are difficult to solve when the convection term dominates because most solution methods give solutions which oscillate in space. Previous criteria based on the one-dimensional convection–diffusion equation have shown that finite difference and Galerkin (linear or quadratic basis functions) will not give oscillatory solutions provided the Peclet number times the mesh size (Pe Δx) is below a critical value. These criteria are based on the solution at the nodes, and ensure that the nodal values are monotone. Similar criteria are developed here for other methods: quadratic Galerkin with upwind weighting, cubic Galerkin, orthogonal collocation on finite elements with quadratic, cubic or quartic polynomials using Lagrangian interpolation, cubic or quartic polynominals using Hermite interpolation, and the method of moments. The nodal values do not oscillate for collocation or moments methods with Hermite cubic polynomials regardless of the value of Pe Δx. A new criterion is developed for all methods based on the monotonicity of the solutions throughout the domain. This criterion is more restrictive than one based only on the nodal values. All methods that are second order (Δx²) or better in truncation error give oscillatory solutions (based on the entire domain) unless Pe Δx is below a critical value. This value ranges from 2 for finite difference methods to 4·6 for Hermite, quartic, collocation methods.     

Stabilized finite element methods for vertically averaged multiphase flow for carbon sequestration

A computationally efficient numerical model that describes carbon sequestration in deep saline aquifers is presented. The model is based on the multiphase flow and vertically averaged mass balance equations, requiring the solution of two partial differential equations – a pressure equation and a saturation equation. The saturation equation is a nonlinear advective equation for which the application of Galerkin finite element method (FEM) can lead to non‐physical oscillations in the solution. In this article, we extend three stabilized FEM formulations, which were developed for uncoupled systems, to the governing nonlinear coupled PDEs. The methods developed are based on the streamline upwind, the streamline upwind/Petrov–Galerkin and the least squares FEM. Two sequential solution schemes are developed: a single step and a predictor–corrector. The range of Courant numbers yielding smooth and oscillation‐free solutions is investigated for each method. The useful range of Courant numbers found depends upon both the sequential scheme (single step vs predictor–corrector) and also the time integration method used (forward Euler, backward Euler or Crank–Nicolson). For complex problems such as when two plumes meet, only the SU stabilization with an amplified stabilization parameter gives satisfactory results when large time steps are used. Copyright © 2016 John Wiley & Sons, Ltd.     

An adaptive solution of the 3-D Euler equations on an unstructured grid

Summary A new algorithm to generate the unstructured grid on a curved surface is developed. The advancing front method is used to generate the tetrahedral meshes in the space. An adaptive grid technique is used to enhance the calculation efficiency. The AUSM⁺ (Advection Upstream Splitting Method) scheme which was developed on a structured grid has been extended to be used to the spatial discretization of a cell-centered finite volume formulation on the unstructured grid. A second order spatial accuracy is achieved by applying a novel cell reconstruction procedure which can prevent the solution from exhibiting spurious oscillations without adding a limiter. A 3-D Euler solver for an adaptive tetrahedral grid and numerical results for several cases are presented.     

Operator splitting and upwinding for the Navier-Stokes equations

We present an operator splitting scheme for the unsteady Navier-Stokes equations for incompressible viscous fluid flow. Like other operator splitting methods applied to these equations, the difficulties associated with the nonlinearity and the incompressibility condition are decoupled. At each time step we obtain two subproblems of Stokes type and a linear one of elliptic type. The linear problem gives us uncoupled scalar problems of transport type; then, we may take advantage of well known upwind techniques for such kind of problems in order to handle large Reynolds numbers flow with coarse meshes. To show the efficiency of the scheme we report numerical results up to Reynolds numbers Re=4000 obtained with very coarse meshes.