A perturbational h4 exponential finite-difference scheme for the convective diffusion equation

A perturbational h4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes, the h4 accuracy of the perturbational scheme is verified using double precision arithmetic.

H4 exponential finite-difference scheme for convective diffusion-equations

Perturbations are applied to the convective coefficients and source term of a convection-diffusion equation so that second-order corrections may be applied to a second-order exponential scheme. The basic Structure of the equations in the resulting fourth-order scheme is identical to that for the second order. Furthermore, the calculations are quite simple as the second-order corrections may be obtained in a single pass using a second-order scheme. For one to three dimensions, the fourth-order exponential scheme is unconditionally stable. As examples, the method is applied to Burgers' and other fluid mechanics problems. Compared with schemes normally used, the accuracies are found to be good and the method is applicable to regions with large gradients.

Numerical-Value Perturbation Method with Application of Solving Convective-Diffusion Integral Equation

The convective--diffusion equation is of primary importance in such fields as fluid dynamics and heat transfer hi the numerical methods solving the convective-diffusion equation, the finite volume method can use conveniently diversified grids (structured and unstructured grids) and is suitable for very complex geometry The disadvantage of FV methods compared to the finite difference method is that FV-methods of order higher than second are more difficult to develop in three-dimensional cases. The second-order central scheme (2cs) offers a good compromise among accuracy, simplicity and efficiency, however, it will produce oscillatory solutions when the grid Reynolds numbers are large and then very fine grids are required to obtain accurate solution. The simplest first-order upwind (IUW) scheme satisfies the convective boundedness criteria, however. Its numerical diffusion is large. The power-law scheme, QMCK and second-order upwind (2UW) schemes are also often used in some commercial codes. Their numerical accurate are roughly consistent with that of ZCS. Therefore, it is meaningful to offer higher-accurate three point FV scheme. In this paper, the numerical-value perturbational method suggested by Zhi Gao is used to develop an upwind and mixed FV scheme using any higher-order interpolation and second-order integration approximations, which is called perturbational finite volume (PFV) scheme. The PFV scheme uses the least nodes similar to the standard three-point schemes, namely, the number of the nodes needed equals to unity plus the face-number of the control volume. For instanc6, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D problems, 2~Dand 3-D flow model equations. Comparing with other standard three-point schemes, The PFV scheme has much smaller numerical diffusion than the first-order upwind (IUW) scheme, its numerical accuracy are also higher than the second-order central scheme (2CS), the power-law scheme (PLS), the QUICK scheme and the second-order upwind(ZUW) scheme.

Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme

A new finite difference method for the discretization of the incompressible Navier-Stokes equations is presented. The scheme is constructed on a staggered-mesh grid system. The convection terms are discretized with a fifth-order-accurate upwind compact difference approximation, the viscous terms are discretized with a sixth-order symmetrical compact difference approximation, the continuity equation and the pressure gradient in the momentum equations are discretized with a fourth-order difference approximation on a cell-centered mesh. Time advancement uses a three-stage Runge-Kutta method. The Poisson equation for computing the pressure is solved with preconditioning. Accuracy analysis shows that the new method has high resolving efficiency. Validation of the method by computation of Taylor's vortex array is presented.

Fourth order accurate compact scheme with group velocity control (GVC)

For solving complex flow field with multi-scale structure higher order accurate schemes are preferred. Among high order schemes the compact schemes have higher resolving efficiency. When the compact and upwind compact schemes are used to solve aerodynamic problems there are numerical oscillations near the shocks. The reason of oscillation production is because of non-uniform group velocity of wave packets in numerical solutions. For improvement of resolution of the shock a parameter function is introduced in compact scheme to control the group velocity. The newly developed method is simple. It has higher accuracy and less stencil of grid points.

Scheme Construction with Numerical Flux Residual Correction (NFRC) and Group Velocity Control (GVC)

For simulating multi-scale complex flow fields like turbulent flows, the high order accurate schemes are preferred. In this paper, a scheme construction with numerical flux residual correction (NFRC) is presented. Any order accurate difference approximation can be obtained with the NFRC. To improve the resolution of the shock, the constructed schemes are modified with group velocity control (GVC) and weighted group velocity control (WGVC). The method of scheme construction is simple, and it is used to solve practical problems.

Optimized Group Velocity Control Scheme and DNS of Decaying Compressible Turbulence of Relative High Turbulent Mach Number

To overcome the difficulty in the DNS of compressible turbulence at high turbulent Mach number, a new difference scheme called GVC8 is developed. We have succeeded in the direct numerical simulation of decaying compressible turbulence up to turbulent Mach number 0.95. The statistical quantities thus obtained at lower turbulent Mach number agree well with those from previous authors with the same initial conditions, but they are limited to simulate at lower turbulent Mach numbers due to the so-called start-up problem. The energy spectrum and coherent structure of compressible turbulent flow are analysed. The scaling law of compressible turbulence is studied. The computed results indicate that the extended self-similarity holds in decaying compressible turbulence despite the occurrence of shocklets, and compressibility has little effects on relative scaling exponents when turbulent Mach number is not very high.

Experimental Study on Convective Boiling Heat Transfer in Narrow-Gap Annulus Tubes

Since convective boiling or highly subcooled single-phase forced convection in micro-channels is an effective cooling mechanism with a wide range of applications, more experimental and theoretical studies are required to explain and verify the forced convection heat transfer phenomenon in narrow channels. In this experimental study, we model the convective boiling behavior of water with low latent heat substance Freon 113 (R-113), with the purpose of saving power consumption and visualizing experiments. Both heat transfer and pressure drop characteristics were measured in subcooled and saturated concentric narrow gap forced convection boiling. Data were obtained to qualitatively identify the effects of gap size, pressure, flow rate and wall superheat on boiling regimes and the transition between various regimes. Some significant differences from unconfined forced convection boiling were found,and also, the flow patterns in narrow vertical annulus tubes have been studied quantitatively.

An incremental micromechanical scheme for nonlinear particulate composites

A general incremental micromechanical scheme for the nonlinear behavior of particulate composites is presented in this paper. The advantage of this scheme is that it can reflect partly the effects of the third invariant of the stress on the overall mechanical behavior of nonlinear composites. The difficulty involved is the determination of the effective compliance tensors of the anisotropic multiphase composites. This is completed by making use of the generalized self-consistent Mori-Tanaka method which was recently developed by Dai et al. (Polymer Composites 19(1998) 506-513; Acta Mechanica Solida 18 (1998) 199-208). Comparison with existing theoretical and numerical results demonstrates that the present incremental scheme is quite satisfactory. Based on this incremental scheme, the overall mechanical behavior of a hard-particle reinforced metal matrix composite with progressive particle debonding damage is investigated.

An Improved Ce/Se Scheme And Its Application To Detonation Propagation

An improved two-dimensional space-time conservation element and solution element ( CE/ SE) method with second-order accuracy is proposed, examined and extended to simulate the detonation propagations using detailed chemical reaction models. The numerical results of planar and cellular detonation are compared with corresponding results by the Chapman-Jouguet theory and experiments, and prove that the method is a new reliable way for numerical simulations of detonation propagation.

A high order accurate difference scheme for complex flow fields

A high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented. The reason for oscillation production in numerical solutions is analyzed, It is caused by a nonuniform group velocity of wavepackets. A method of group velocity control for the improvement of the shock resolution is presented. In numerical simulation the fifth-order accurate upwind compact difference relation is used to approximate the derivatives in the convection terms of the compressible N-S equations, a sixth-order accurate symmetric compact difference relation is used to approximate the viscous terms, and a three-stage R-K method is used to advance in time. In order to improve the shock resolution the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets. (C) 1997 Academic Press.

Convective coupled map for simulating spatiotemporal chaos in flows

A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper to simulate spatiotemporal chaos in fluid hows. It is found that the parameter region of spatiotemporal chaos can be determined by the maximal Liapunov exponent of its complexity time series. This simple model implies a similar physical mechanism for turbulence such that the route to spatiotemporal chaos in fluid hows can be envisaged.

Air flow over a mountain and the convective boundary-layer

In this paper, the analytical model coupling the convective boundary layer (CBL) with the free atmosphere developed by Qi and Fu (1992) is improved. And by this improved model, the interaction between airflow over a mountain and the CBL is further discussed. The conclusions demonstrate: (1) The perturbation potential temperatures in the free atmosphere can counteract the effect of orographic thermal forcing through entraining and mixing in the CBL. If u(M)BAR > u(F)BAR, the feedback of the perturbation potential temperatures in the free atmosphere is more important than orographic thermal forcing, which promotes the effect of interfacial waves. If u(M)BAR < u(F)BAR, orographic thermal forcing is more important, which makes the interfacial height and the topographic height identical in phase, and the horizontal speeds are a maximum at the top of the mountain. (2) The internal gravity waves propagating vertically in the free atmosphere cause a strong downslope wind to become established above the lee slope in the CBL and result in the hydraulic jump at the top of the CBL. (3) With the CBL deepening, the interfacial gravity waves induced by the potential temperature jump at the top of the CBL cause the airflow in the CBL to be subcritical.