MATHEMATICAL MODELING OF STEADY FLOW PAST CIRCULAR CYLINDER WITH SPLITTER PLATES BY R-FUNCTIONS METHOD

Abstract

In the paper the steady flow of a viscous incompressible fluid past a circular cylinder with attached splitter plates is considered. The mathematical representation of the problem takes the form of an external boundary value problem for the stream function. To solve the problem, a numerical method combining the R-functions and the nonlinear Galerkin method is used. The R-functions method is employed to construct a problem solution structure that exactly satisfies all the boundary conditions of the problem and has the required behavior at infinity. The Galerkin method is then applied to approximate the undetermined components of this structure, ensuring accuracy and efficiency in the solution process. A series of computational experiments was conducted to investigate the flow past a single circular cylinder and past a circular cylinder with triangular and rectangular splitter plates at various Reynolds numbers. For the case of a single cylinder, a quantitative error analysis confirms the convergence of the numerical method, with relative errors dropping below 1% when using a moderate number of basis functions. The computational cost remains practical, with each solution obtained in approximately 11 minutes on a standard workstation. Drag and lift coefficients are computed for the single-cylinder case, allowing for quantitative assessment of aerodynamic performance and validation of the numerical model against known reference data. The influence of splitter plate geometry on the flow structure is explored through visualizations, highlighting changes in vortex patterns and symmetry. The proposed approach demonstrates strong numerical accuracy and computational robustness for the single-cylinder case and offers a flexible framework for studying external viscous flows with complex boundary configurations.

Keywords: Viscous incompressible fluid, External boundary value problem, Stream function, R-functions method, Nonlinear Galerkin method.