Browsing by Subject "BEM"

Now showing 1 - 3 of 3

Open Access
Isogeometric and NURBS-enhanced boundary element formulations for steady-state heat conduction with volumetric heat source and nonlinear boundary conditions
(Elsevier, 2022-12) Gümüş, Özgür Can; Baranoğlu, B.; Çetin, Barbaros
Boundary Element Method (BEM) is a numerical tool that is applied to many different types of engineering problems. BEM possesses several advantages over other numerical methods such as boundary-only discretization and its semi-analytical nature. Application of Isogeometric Analysis (IGA) to BEM is a recently proposed computational method where the main purpose is to use geometrical basis functions as the shape functions of field variables. Key features of combining these two techniques are the exact representation of the geometry, elimination or suppression of the meshing procedure, reduction of the problem dimension and obtaining highly accurate results especially for the flux values on the boundaries compared to conventional BEM. In this study, steady-state heat conduction problems with nonlinear boundary condition and surface heat source are analyzed where geometries are formed by NURBS, and field variables are described with Lagrangian (constant and quadratic) basis functions and NURBS basis functions. Convergence rates and CPU time of different types of element representations are discussed which eventually reveals the performance and capabilities of IGABEM.
Open Access
A multi-domain direct boundary element formulation for particulate flow in microchannels
(Elsevier Ltd, 2021-11-01) Topuz, Alper; Baranoğlu, B.; Çetin, Barbaros
In the present study, a multi-domain boundary element formulation is developed for high surface-area-to-volume ratio problems (i.e. particulate flow in high aspect ratio microfluidic channels, in a porous medium or in microfluidic devices with repetitive structures). The solution domain is decomposed into subdomains and the variable condensation technique is implemented. The solution matrices are built for each subdomain, and the matrices are updated at each time step only for the subdomains in which the particles move at each time step. Ghost domains, which are fictitious domains encapsulating the interfaces between the subdomains, are also introduced in the formulation to treat the particles crossing the interfaces between the subdomains. The formulation reveals that the computation of the subdomain matrices is further simplified for solution domains composed of periodic structures. The results of our study revealed that speed-up values as high as 50 is achievable with the current formulation.
Open Access
A multi-domain direct boundary element formulation for particulate flow in microchannels
(2021-08) Topuz, Alper
In the present study, a multi-domain boundary element formulation is developed for high surface-area-to-volume ratio problems (i.e. particulate ﬂow in high as-pect ratio microﬂuidic channels, in a porous medium or in microﬂuidic devices with repetitive structures). The solution domain is decomposed into subdomains and the variable condensation technique is implemented. The solution matrices are built for each subdomain, and the matrices are updated at each time step only for the subdomains in which the particles move at each time step. Ghost domains, which are ﬁctitious domains encapsulating the interfaces between the subdomains, are also introduced in the formulation to treat the particles cross-ing the interfaces between the subdomains. The formulation reveals that the computation of the subdomain matrices is further simpliﬁed for solution domains composed of periodic structures. The results of our study revealed that speed-up values as high as 50 for 2D structures and 80 for 3D structures is achievable with the current formulation.