Iskanje po katalogu digitalne knjižnice

Opis: The development of new numerical methods for fluid flow simulations is challenging but such tools may help to understand flow problems better. Here, the Boundary-Domain Integral Method is applied to simulate laminar fluid flow governed by a dimensionless velocity–vorticity formulation of the Navier–Stokes equation. The Reynolds number is chosen in all examples small enough to ensure laminar flow conditions. The false transient approach is utilized to improve stability. As all boundary element methods, the Boundary-Domain Integral Method has a quadratic complexity. Here, the ℋ2 -methodology is applied to obtain an almost linear complexity. This acceleration technique is not only applied to the boundary only part but more important to the domain related part of the formulation. The application of the ℋ2 -methodology does not allow to use the rigid body method to determine the singular integrals and the integral free term as done until now. It is shown how to apply the technique of Guigiani and Gigante to handle the strongly singular integrals in this application. Further, a parametric study shows the influence of the introduced approximation parameters. For this purpose the example of a lid driven cavity is utilized. The second example demonstrates the performance of the proposed method by simulating the Hagen–Poiseuille flow in a pipe. The third example considers the flow around a rigid cylinder to show the behavior of the method for an unstructured grid. All examples show that the proposed method results in an almost linear complexity as the mathematical analysis promisses.
Ključne besede: boundary-domain integral method, velocity–vorticity, adaptive cross approximation, modified helmholtz equation, Yukawa potential, fast multipole method, ℋ-structure
Objavljeno v DKUM: 28.11.2024; Ogledov: 0; Prenosov: 4
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Opis: In dispersed multiphase flow processes we encounter coupled heat, mass and momentum transfer between the disoersed and the continuous phase. In the context of the subdomain Boundary Domain Integral Method (BDIM) solution of the Navier-Stokes equations a two-way coupling model is presented based on the use of the elliptic fundamental solution and the Dirac delta function properties which leads to accurate evaluation of the heat and mass point particle source impacts on the continuous (air) phase. In addition, the two-phase flow case under consideration is extended to the case of porous spherical particle drying with internal moving drying front, which is solved by the Boundary Element Method (BEM).
Ključne besede: heat transfer, mass transfer, Boundary Element Methods
Objavljeno v DKUM: 01.07.2024; Ogledov: 113; Prenosov: 15
Celotno besedilo (1,10 MB)
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Ključne besede: boundary-domain integral method, dispersed two-phase flow, two-way coupling, spherical porous particles, drying
Objavljeno v DKUM: 28.03.2024; Ogledov: 217; Prenosov: 17
Celotno besedilo (1,81 MB)
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Opis: Robust, automated mesh generation on arbitrary weld joint geometries, using finite element method (FEM) is a problematic task. It was previously discovered, that an arbitrary weld joint geometry can be parameterized inside a CAD environment [1], however when it comes to domain discretization and boundary conditions assignment, the parameterized approach becomes too demanding inside FEM. This results in long FEM model preparation times and sometimes in problems with the parametric model itself, which leads to a need for an additional numerical method - boundary element method (BEM), which overcomes this issue and is beneficial in this case. BEM is a numerical method, that in addition to other applications finds a use in the elasto-mechanic problems, where the only concern is the boundary of the considered geometric domain. Since notch stress calculations of weld joints fall into this category, their calculation can be carried out with it. Since there is not much available information on whether or not such calculations are a suitable alternative for the currently used FEM, this thesis had to be confirmed through a structured and step by step procedure. First, a notch mesh quality study has been made, then other entities followed. It was discovered that BEM is applicable to the problem and capable of calculating results with sufficient quality. Furthermore, the parameter driven approach and automated calculation provide for additional advantageous potentials.
Ključne besede: weld joint, boundary element method, finite element method, spatial discretization, notch stress
Objavljeno v DKUM: 02.11.2022; Ogledov: 549; Prenosov: 0
Celotno besedilo (4,62 MB)

Opis: Analytical solutions were derived for the non-linear, one-dimensional consolidation equations for unsaturated soils. The governing equations with a non-homogeneous mixed-boundary condition were presented, in which the water flow was assumed to be governed by a non-Darcy law, whereas the air flow followed the Darcy law. The non-Darcy law was actually the non-linear, flux-gradients relationship. The consolidation equations were thus present in a strong, non-linear way. In order to analytically solve the equation, a homotopy analysis method (HAM) was introduced in the study, which is an analytical technique for nonlinear problems. Firstly, a governing equation in a dimensionless form was derived for a one-dimensional consolidation under unsaturated soils. The method was then used for a mapping technique to transfer the original nonlinear differential equations to a number of linear differential equations. These differential equations were independent with respect to any small parameters, and were convenient for controlling the convergence region. After this transferring, a series solution to the equations was then obtained using the HAM by selecting the linear operator and the auxiliary parameters. Meanwhile, comparisons between the analytical solutions and the results of the finite-difference method indicate that the analytical solution is more efficient. Furthermore, our solutions indicate that the dissipation of air pressure is much faster than that of water pressure, and the values for the threshold gradient I have obvious effects on the dissipation values of the excess pore-water pressure, but no significant effect on that of the excess pore-air pressure.
Ključne besede: unsaturated soil, homotopy analysis method, analytical solutions, non-Darcy law, initial and boundary conditions
Objavljeno v DKUM: 14.06.2018; Ogledov: 1471; Prenosov: 114
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