Three-point scheme and two-point boundary formulations for unsteady diffusion with flow

^** Email: ron.smith{at}lboro.ac.uk A three-point scheme of Crank–Nicolson type and two-pointboundary formulations are derived that accurately model bothlong- and short-scale branches of gradual time-variation solutionsfor unsteady diffusion on low-resolution grids. Inadequaciesin the resolution are compensated, to second order in the rateof change, with interior and boundary weights that have elementaryfunction dependence on the grid spacing. Numerical testing suggeststhat the computations are robust to rapid variation, improvewith interior grid points at tuned uniform spacing and becomeaccurate if the design assumption of gradual time variationis satisfied.     

拉格朗日高阶中心型守恒气体动力学格式

提出了拉格朗日高阶中心型守恒气体动力学格式。用产生于当前时刻子网格密度和当前时刻网格声速的子网格压力构造了子网格力,用加权本质无震荡方法构造的高阶子网格力构造了高阶空间通量,借助时间中点通量的泰勒展开完成了高阶时间通量离散,利用动量守恒条件使得格点速度以与网格面的数值通量相容的方式计算。编制了拉格朗日高阶中心型守恒气体动力学格式,对Saltzman活塞问题进行了数值模拟,数值结果表明,拉格朗日高阶中心型守恒气体动力学格式的有效性和精确性.     

扩散方程保正的有限体积格式

在大变形网格上数值求解多介质扩散方程时, 如何构造具有保正性的扩散格式一直是人们关注的难题. 本文将简要综述与保正性相关的扩散格式的研究历史, 并为解决这一难题提出新的设计途径,构造出新的具有较高精度的单元中心型守恒保正格式, 它们可兼顾网格几何变形和物理量变化. 本文将给出数值实验结果, 验证新格式在变形的网格上保持非负性.     

MFCAV近似Riemann解在新型拉氏方法中的应用

Maire等提出了一种新型的有限体积中心型拉氏方法, 该方法大大地改善了一直困扰着一般中心型拉氏方法的虚假网格变形. 然而在计算数值流和移动网格时,该方法只应用了数值黏性较大的弱波近似(weak wave approximatedmethod, WWAM) Riemann解, 而且方法的设计表明其他类型的近似Riemann解不能简单直接地应用上去. 将体平均多流管(multifluid channel on averaged volume, MFCAV)近似Riemann解视为对WWAM的修正,成功将其应用于新型方法中, 数值实验表明应用了MFCAV 的新方法是有效的. 研究为将其他更为有效的近似Riemann解应用于该新型方法中开辟了一条道路.      

基于特征理论的二维可压缩流动的二阶拉氏算法

提出一种求解二维拉氏可压缩流体力学方程的中心型二阶精度有限体积方法.利用特征理论构造网格节点处的局部近似演化算子,算子用来求解网格节点处的速度及压力,利用这些物理量更新节点位置及计算网格界面通量.通过结合一定的重构方案,该方法达到时、空二阶精度,并且形式简单、计算量小,适用于结构网格与非结构网格.典型数值实验表明,本文格式具有良好的收敛性、对称性及鲁棒性,且能自然地求解多物质流动问题.     

Lagrangian cell-centered conservative scheme

This paper presents a Lagrangian cell-centered conservative gas dynamics scheme. The piecewise constant pressures of cells arising from the current time sub-cell densities and the current time isentropic speed of sound are introduced. Multipling the initial cell density by the initial sub-cell volumes obtains the sub-cell Lagrangian masses, and dividing the masses by the current time sub-cell volumes gets the current time sub-cell densities. By the current time piecewise constant pressures of cells, a scheme that conserves the momentum and total energy is constructed. The vertex velocities and the numerical fluxes through the cell interfaces are computed in a consistent manner due to an original solver located at the nodes. The numerical tests are presented, which are representative for compressible flows and demonstrate the robustness and accuracy of the Lagrangian cell-centered conservative scheme.     

一类格心型ALE有限体积格式方法

现在国内外流行的ALE有限体积格式基本上都基于交错网榕进行格式的离散.该类格武在进行重映时,速度、密度和能量需要分别进行重映计算,效率较低,而且由于速度在网格角点.而密度、能量在网格中心,重映时会出现动能和内能不协调现泉.本文在巳有格心型Lagrange有限体积格式研究的基础上,结合Abgrall R.等关于榕心型格式下的网格角点速度的计算方法,利用最小二乘法进行高阶插值多项式重构,构造了一类新的格心型的高精度Lagrangian有限体积格式,并结合有效的高精度ENO守恒重映方法,获得了一类格心型的高精度ALE有限体积格式.数值试验的结果说明本文的格式是有效的,高精度的,收敛的,并且避免了物理量的不协调现象.     

基于特征理论的二维无粘Lagrange流体力学有限体积法

提出一个求解二维无粘Lagrange流体力学方程的中心型有限体积方法.采用特征理论求解网格节点处的速度及压力,并利用这些物理量更新节点位置及计算网格界面通量.方法适用于结构网格与非结构网格.典型数值实验的结果表明,格式具有较好的收敛性、对称性、能量守恒性及鲁棒性,且能自然地求解多物质流动问题.     

Convergence analysis of a finite volume method via a new nonconforming finite element method

The article is devoted to the study of convergence properties of a Finite Volume Method (FVM) using Voronoi boxes for discretization. The approach is based on the construction of a new nonconforming Finite Element Method (FEM), such that the system of linear equations coincides completely with that for the FVM. Thus, by proving convergence properties of the FEM, we obtain similar ones of the FVM. In this article, the investigations are restricted to the Poisson equation. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:213–231, 1998