High-Resolution Finite Compact Difference Schemes for Hyperbolic Conservation Laws

A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknown variable for third-order FC-ENO scheme and two unknown variables for fifth-order FC-ENO scheme. Numerical test results of the proposed FC-scheme were compared with traditional TVD, ENO and WENO schemes to demonstrate its high-order accuracy and high-resolution.

小型气驱动式U形振荡水槽

本文介绍气驱动式U形振荡水楷(U形管)的设计特点、流场品质和初步实验结果。在结构设计上采用了理论计算的弯管型线、步进电机带动蝶阀的控制系统和吸气驱动等较先进的技术措施,使得该设备具有流场品质好、结构简单、调节方便等优点,是开展振荡流实验研究的基本设备。

用LDA测量U形水槽内的振荡流

本文介绍LDA用于测量U形水槽内的振荡流。水槽直管段为正方形,弯管段内侧弯面及外侧弯面是专门计算设计的。对于水平直管段、竖管段及弯管段共七个截面,测量了边界层外振荡流速的振幅分布。对于水平直管段上底面及下底面各三个截面,测量了边界层內振荡流速的振幅分布及相位分布。测量结果和无限长槽道的理论计算结果作了比较,二者基本符合。

A Multiscale-Domain Decomposition Method for High Reynolds Number Flows

The high Reynolds number flow contains a wide range of length and time scales, and the flow domain can be divided into several sub-domains with different characteristic scales. In some sub-domains, the viscosity dissipation scale can only be considered in a certain direction; in some sub-domains, the viscosity dissipation scales need to be considered in all directions; in some sub-domains, the viscosity dissipation scales are unnecessary to be considered at all. For laminar boundary layer region, the characteristic length scales in the streamwise and normal directions are L and L Re-1/ 2 , respectively. The characteristic length scale and the velocity scale in the outer region of the boundary layer are L and U, respectively. In the neighborhood region of the separated point, the length scale l<conservation equations for discrete cells was proposed and named the discrete fluid dynamics (DFD) algorithm. Analysis shows that the basic conservative equations for discrete cells are the Euler equations, NS- and diffusion parabolized (DP) NS equations. In this paper, a new multiscale-domain decomposition method is developed for the high Reynolds number flow. First, the whole domain is decomposed to different sub-domains with the different characteristic scales. Then the different dominant equation of all sub-domains is defined according to the diffusion parabolized (DP) theory of viscous flow. Finally these different equations are solved simultaneously in whole computational region. For numerical tests of high Reynolds numerical flows, two-dimensional supersonic flows over rearward and frontward steps as well as an interaction flow between shock wave and boundary layer were solved numerically. The pressure distributions and local coefficients of skin friction on the wall are given. The numerical results obtained by the multiscale-domain decomposition algorithm are well agreement with those by NS equations. Comparing with the usual method of solving the Navier-Stokes equations in the whole flow, under the same numerical accuracy, the present multiscale domain decomposition method decreases CPU consuming about 20% and reflects the physical mechanism of practical flow more accurately.