T -functions for 2-D creeping flow on domains with circular cylinders, corners, and possessing symmetry

Abstract

The purpose of the paper is to propose of a way of constructing trial functions for the indirect Trefftz method as applied to 2-D creeping (Stokes) flow problems. The considered cases refer to the problems of flow around fixed and rotating circular cylinders, in corners with two walls fixed, or one wall moving, and flow possessing particular symmetry. The trial functions, proposed and systematically constructed fulfil exactly not only the governing equation, like T-complete Herrera functions, but also certain given boundary conditions and conditions resulting from assumed symmetry. A list of such trial functions, unavailable elsewhere, is presented. The derived functions can be treated as a subset of T-complete Herrera functions, which can be used for solving typical boundary-value problems.