Equations of Laminar and Turbulent Flows in General Curvilinear Coordinates.
Marshall C. Richmond, H. C. Chen, V. C. Patel · Defense Technical Information Center (DTIC) · 1986
Recent developments in computational fluid mechanics and grid generation have made it possible to consider complex three dimensional laminar and turbulent flows using nonorthogonal coordinates. However, the necessary equations in generalized nonorthogonal coordinates. However, the necessary equations in generalized nonorthogonal are not readily available in a single reference. The purpose of this report is to present these equations for an incompressible fluid. Methods of curvilinear tensor analysis are used to develop the most commonly used equations. Their relationship with the more familiar equations in orthogonal coordinates is shown. Finally, the practical problems of evaluating the many geometric coefficients which appear in these equations are examined by considering numerically generated coordinates for flow around three dimensional bodies. Keywords: Tensor analysis; General curvilinear coordinates; Equations of fluid motion; Turbulence models; Body fitted coordinates; and Computational fluid dynamics.