摘要
Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程及能量方程的数值解结果必须通过有限差分或有限容积法的公式才能精确表示，因为对于确定流动与换热的特性而言，固体表面附近的区域一般地说是起主导作用的，在固体表面上或其附近的流速与换热直接取决于固体表面附近区域中较大的梯度，要精确地确定流速与换热就需要能正确地表述这些较大的梯度值。在大多数工程问题中常常会碰到不规则形状的结构，这些不规则形状的边界无法用直角坐标、圆柱坐标及球坐标中的任何一个坐标系来描述，Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程及能量方程的数值解结果常常是用三种最通用的坐标系（直角坐标、圆柱坐标及球坐标）之一来逼近不规则形状的边界而得出的，在这一近似处理过程中，常常采用不规则形状的面积或体积保持不变的原则．缩小网格的尺寸一般可以改进逼近的精度，却因此增加了计算机的运行时间．尽管如此，采用这种近似处理方法仍然不能保证总可获得到合理的解。文中提供了一种采用适体坐标转换的方法。它可以把物理空间中的一个任意三维几何区域变换成转换空间中的一个矩形或圆柱状区域，这种转换的独特的优点是所有物理的边界是与计算节点相重合的，因此，可为Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程及能量方程提供精确而且高效的数值解?
The numerical solution of the Navier-Stokes and energy equations must be representedaccurately in the finite-difference or finite-volume formulation,for the region in the immedi-ate vicinity of solid surfaces is generally dominant in determining the character of flow andheat transfer.The velocity and heat transfer on or near solid surfaces are directly dependenton the large gradients that prevail in this region near the surface,and accurate determinationof velocity and heat transfer requires that these large gradients be represented correctly.Irregular shape of structures is often encountered in most engineering problems.Theseirregular boundary shapes cannot be described by any one of the Cartesian,cylindrical,andspherical-coordinate representations.Numerical solutions of the Navier-Stokes and energy e-quations are obtained by approximating irregular boundary shapes with one of the most suitable coordinate systems of Cartesian, cylindrical,and spherical.In the process of this ap-proximation,either conservation of surface or volume of the irregular shape is usually em-ployed-Accuracy of this approximation is in general improved by using reduced mesh sizeand thus increases computer running time.However,there is no assurance of obtaining areasonable solution all the time by this approximation.A method using boundary-fitted coordinate transformation is presented.It has the capa-bility to transform arbitrary 3-D geometries in a physical domain to either a rectangular orcylindrical shape in the transformed space. The unique advantage of this transformation isthat all physical boundaries are coincident with the computational grids i thus , it will give anaccurate and efficient numerical solution to the Navier-Stokes and energy equations. A pro-cedure for coordinate generation is outlined , and the transformed Navier-Stokes and energyequations are presented.While the boundary-fitted coordinate transformation has many advantages but the trans-formation itself is not unique. In order to accomplish a successful transformati
出处
《西安交通大学学报》
EI
CAS
CSCD
北大核心
1994年第5期41-50,共10页
Journal of Xi'an Jiaotong University
基金
国立阿贡实验室多相流研究所
关键词
能量方程
适体坐标
传热
N-S方程
Navier-Stokes equation energy equation boundary fitted coordinateheat trans fer
