1 Copyright © 2003 by ASME Proceedings of FEDSM’03 4TH ASME_JSME Joint Fluids Engineering Conference Honolulu, Hawaii, USA, July 6–11, 2003 FEDSM2003-45526 A MASS CONSERVATIVE STREAMLINE TRACKING METHOD FOR THREE DIMENSIONAL CFD VELOCITY FIELDS Zhenquan Li Department of Mechanical Engineering The University of Auckland Private Bag 92019, Auckland New Zealand ABSTRACT Mass conservation is a key issue for accurate streamline visualization of flow fields. This paper presents a mass conservative streamline construction method for CFD velocity fields defined at discrete locations in three dimensions for incompressible flows. Linear mass conservative interpolation is used to approximate velocity fields. Demonstration examples are shown. INTRODUCTION Methods for the visualization of fluid flows have attracted much attention from different areas such as computer science and engineering. Streamline visualization is an important instrument for exploring the properties of a fluid velocity field. A streamline is everywhere tangential to the velocity field V , i.e., a graph of the solution of: 3 3 2 2 1 1 v dx v dx v dx = = if ( 29 3 2 1 0 , , = ≠ i v i or written in vector form as V X = dt d (1) using a Cartesian coordinate system ( 29 3 2 1 x x x , , where ( 29 3 2 1 v v v , , V = . The integration of (1) is usually solved numerically and involves schemes for both the interpolation of the velocity field and time integration [1- 4]. Provided 4th order Runge Kutta schemes (or better) are used for time integration the more significant source of error arises from velocity interpolation [5]. In particular, failure to conserve mass can produce errors that cannot be eliminated by reducing the integration step and which can generate artificial effects, such as false spiraling [5]. Thus, the computation is generally a complicated and inefficient process [4,6,7]. A CFD velocity field is defined at discrete locations in space. It is assumed that the discrete velocity field is an approximation to a continuous mass conservative velocity field in the same domain. Often quite simple interpolation strategies are used, a common one being a locally linear interpolation of the velocity. Linear interpolation of the velocity over each cell in a mesh is a mathematical approximation and the resulting field does not necessarily satisfy mass conservation. There are a number of mass conservative streamline construction methods for steady flows [6,7,8] in three dimensions. All these methods are based on the formula given in [9]: for a steady compressible fluid, there exist two stream functions f and g such that the momentum g f ∇ × ∇ = ρV (2) where ρ is the fluid density. The surfaces represented by holding f or g constant are called stream surfaces. A streamline is the intersection of two stream surfaces. The steady compressible fluid flow expressed by (2) obeys the law of mass conservation. Recently Feng et al [8] described a technique whereby streamlines and stream surfaces are generated by linear mass conservative interpolation schemes for the CFD velocity field for incompressible flows. Even though their technique is useful for the computer visualization of three-dimensional velocity fields, there is an important issue regarding their process for generating a mass conservative velocity field from