Numerical Simulation of Viscoelastic Fluid Flow Past a Cylinder on a Streamfunction Coordinate System

• Published in: Journal of computational physics Vol. 108; no. 2; pp. 226 - 235
• Main Authors: Husain, I., Chandna, O.P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.10.1993; Elsevier
• Subjects: 990200 > Mathematics & Computers; Classical and quantum physics: mechanics and fields; Classical mechanics of continuous media: general mathematical aspects; Computational methods in fluid dynamics; COMPUTERIZED SIMULATION; CONFIGURATION; CONFORMAL MAPPING; CYLINDRICAL CONFIGURATION; ENGINEERING; Exact sciences and technology; Fluid dynamics; FLUID FLOW; Fluid mechanics: general mathematical aspects; Fundamental areas of phenomenology (including applications); GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; MAPPING; Mathematical methods in physics; Numerical approximation and analysis; Numerical simulation, solution of equations; Ordinary and partial differential equations, boundary value problems; Physics; SIMULATION; TOPOLOGICAL MAPPING; TRANSFORMATIONS 420400 > Engineering > Heat Transfer & Fluid Flow; VISCOUS FLOW; Viscoelastic fluid; Fluid dynamics; Stream function; Numerical solution; Steady flow; Numerical simulation; Coordinate system; Two dimensional flow; Cylinders
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1006/jcph.1993.1178

Steady two-dimensional flow of a viscoelastic fluid past a streamlined cylinder is numerically modeled using the von Mises coordinates. The governing equations for a second-order fluid flow past the cylinder are first transformed into a steamfunction coordinate system (φ, ψ), where ψ is the streamfuntion of the flow. Taking φ - x, the von Mises coordinates (x, ψ) are obtained and the governing equations reduced to a system of two equations in two unknowns y(x, ψ) and w(x, ψ) which are solved subject to the appropriate boundary conditions in the yon Mises computational domain. Several approximation formulas for the vorticity on the surface of the cylinder are derived and employed in obtaining the solutions at various Reynolds and Weissenberg numbers for two specific cross sections.