A new method for Stokes problems with circular boundaries using degenerate kernel and Fourier series

Abstract

SUMMARYThis study is concerned with the Stokes flow of an incompressible fluid of constant density and viscosity with circular boundaries. To fully capture the circular boundary, the boundary densities in the direct and indirect boundary integral equations (BIEs) are expanded in terms of Fourier series. The kernel functions in either the direct BIE or the indirect BIE are expanded to degenerate kernels by using the separation of field and source points. Consequently, the improper integrals are transformed to series sum and are easily calculated. The linear algebraic system can be established by matching the boundary conditions at the collocation points. Then, the unknown Fourier coefficients can be easily determined. Finally, several examples including circular and eccentric domains are presented to demonstrate the validity of the present method. Five gains were obtained: (1) meshless approach; (2) free of boundary-layer effect; (3) singularity free; (4) exponential convergence; and (5) well-posed model.

Modeling of fluid flow in periodic cell with porous cylinder using a boundary element method

“…The distributions obtained for ψ(x, y) (top) and , [12] and in the present work are compared in negative value for n = 80 at ε c = 0.9 is explained by the very narrow distance between cylinders that becomes approximately equal to the length of boundary linear element.…”

“…at the general point (x, y) can then be calculated from the 95 formulas (10), (12). Taking into account u = ∂ψ/∂y, v = −∂ψ/∂x the formulas for velocity components are written:…”

“…To validate the method developed for a doubly connected domain the flow between eccentric cylinders as considered by [11], [12], see fig. 9, has been modelled.…”

An Analytical Approach for the Green's Functions of Biharmonic Problems with Circular and Annular Domains

“…In the recent years, the Green's function of an isotropic annular plate clamped along one edge and free at the other was solved by Adewale [8]. Following the success of null-field integral formulation for typical BVPs [9][10][11], the present paper provides an analytical approach by using null-field integral equations in conjunction with Fourier series and degenerate kernels to derive the Green's functions of circular and annular plates.…”

Null‐field approach for Laplace problems with circular boundaries using degenerate kernels

“…The exponential convergence rate was proved in the Kress' book [32] for BIEM by using degenerate kernel and Fourier series. Numerical experiments was performed for the Stokes flow [33].…”