Résolution des équations de dispersion–diffusion en présence de forts gradientsResolution of advection–diffusion equation in presence of sharp gradient

In order to resolve the convection terms in the simulation of coastal flows, we propose a numerical method based on the Total Variation Diminishing scheme completed with the Artificial Compression Method to reduce the artificial diffusion and to sharpen the tracer profile in strong gradient regions. This method was applied successfully at discontinuous regions, but out of these regions a limitation of its application is necessary. An application is made to estimate the width of the fresh water band in the Eastern English Channel. To cite this article: C. Sart et al., C. R. Mecanique 330 (2002) 159–165.     

Axisymmetric impingement of a hot jet on a flat plate: equilibrium flow analysis of high-temperature air

The flow structure of an underexpanded supersonic jet with high reservoir temperature impinging on a flat plate has been numerically investigated using a Total Variation Diminishing (TVD) scheme. When the temperature of the flow field is high enough to cause chemical reaction, the specific heat ratio,, is no longer equal to 1.4, nor constant. This explains the difference found in the literature between the flow properties of the calorically perfect gas and that of the chemically reacting flow. Under the equilibrium flow assumption the effect of high temperature gas on the impinging jet has been taken into account in the present paper by using specific heat ratio and speed of sound given by correlation polynomials of thermodynamic variables. The limiting case of cold jet calculation in the present numerical results agreed well with the existing experimental data. For the equilibrium jet with high reservoir temperature,T _o=1000K, qualitative support of the present result has been provided by means of the approximation theory.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

An implicit-explicit upwind algorithm for the parabolized Navier-Stokes equations

In this paper, a second-order implicit-explicit upwind algorithm has been developed for three-dimensional Parabolized Navier-Stokes (PNS) equations. The agreement between the results of the new upwind algorithm and those of the implicit upwind algorithm and its ability in marching a long distance along the streamwise direction have been shown for the supersonic viscous flow past a sphere-cone body. The CPU time is greatly reduced. The project supported by the National Natural Science Foundation of China     

Droplet break-up through an oblique shock wave

The interaction of a two-phase flow with a wedge where a stationary shock wave is initially settled is studied in a two-dimensional configuration. Before the introduction of the dispersed phase, the flow around the wedge is a supersonic one phase flow such as an attached stationary shock wave is present. Then, the dispersed phase is introduced upstream the initial position of the stationary shock wave. The purpose of this study is to point out two-phase and droplets break-up effects on the oblique shock wave. The two-dimensional equations are solved by a TVD scheme where fluxes are computed by using Riemann solver for the gas phase equations and also for the dispersed phase equations wich is an original approach due to the authors (Saurel et al. 1994). In addition to drag forces and heat and mass transfers, the process of droplets fragmentation based on the particle oscillation is considered. Accepted April 28, 1995     

Unsteady supersonic flow over an oscillatory aerofoil using a second-order TVD scheme

The unsteady flow over an oscillatory NACA0012 aerofoil has been simulated by the calculation with Euler equations. The equations are discretized by an implicit Euler in time, and a second-order space-accurate TVD scheme based on flux vector splitting with van Leer's limiter. Modified eigenvalues are proposed to overcome the slope discontinuities of split eigenvalues at Mach = 0·0 and ± 1·0, and to generate a bow shock in front of the aerofoil. A moving grid system around the aerofoil is generated by Sorenson's boundary fitted co-ordinates for each time step. The calculations have been done for two angles of attack θ = 5·0° sin (ωt) and θ = 3·0° + 3·0° sin (ωt) for the free-stream Mach numbers 2·0 and 3·0. The results show that pressure and Mach cells flow along characteristic lines. To examine unsteady effects, the responses of wall pressure and normal force coefficients are analysed by a Fourier series expansion.     

Comparisons of TVD schemes for turbulent transonic projectile aerodynamics computations with a two-equation model of turbulence

The development of a computer program to solve the axisymmetric full Navier--Stokes equations with k-ε two-equation model of turbulence using various total variation diminishing (TVD) schemes is the primary interest of this study. The computations are performed for the turbulent, transonic, viscous flow over a projectile with/without supporting sting at zero angle of attack. The predicted results, as well as the convergence characteristics, by various TVD schemes are compared with each other. The results show that the TVD schemes of higher-order accuracy do have influence on the regions of high gradients such as shock, base corner and base flow. However, the schemes of third-order accuracy do not necessarily improve the agreement with measured data (which is not available on the base) than that of second-order accuracy, but surely generate apparent different result of base flow. The supporting sting on the projectile base will complicate the base flow and the existence of the sting will slightly shift the shock location and slightly change the flow field after the shock. More iteration steps are needed to get the converged results in the computation for the projectile with sting.     

A comparison of spatial discretization schemes for differential solution methods of the radiative transfer equation

A comparison of discretization schemes required to evaluate the radiation intensity at the cell faces of a control volume in differential solution methods of the radiative transfer equation is presented. Several schemes developed using the normalized variable diagram and the total variation diminishing formalisms are compared along with essentially non-oscillatory schemes and genuinely multidimensional schemes. The calculations were carried out using the discrete ordinates method, but the analysis is equally valid for the finite-volume method. It is shown that the S schemes of the genuinely multidimensional family perform quite well, particularly in problems with discontinuous radiation intensity fields. However, they are time consuming, and so they do not always become more attractive regarding the trade-off between accuracy and computational requirements, in comparison with other high-order schemes that, although being less accurate, are also more economical.     

一种具有较小数值耗散的对称TVD格式

为了减小TVD格式的数值粘性,提高TVD格式的分辨度,提出了一种具有较小数值耗散的Harten型TVD格式.数值模拟结果表明,这种Harten型TVD格式比原来的Harten格式^[1]及其改进形式Harten-Yee^[2]的TVD格式能更好地模拟出边界层及涡流.     

带对流项的渗流型方程的隐格式

本文用离散泛函分析方法证明了带对流项的渗流型方程的隐格式差分解的收敛性,同时得到微分方程弱解的存在性     

Convergence of relaxation schemes for hyperbolic conservation laws with stiff source terms

We focus in this study on the convergence of a class of relaxation numerical schemes for hyperbolic scalar conservation laws including stiff source terms. Following Jin and Xin, we use as approximation of the scalar conservation law, a semi-linear hyperbolic system with a second stiff source term. This allows us to avoid the use of a Riemann solver in the construction of the numerical schemes. The convergence of the approximate solution toward a weak solution is established in the cases of first and second order accurate MUSCL relaxed methods.