Purpose – The purpose of this paper is to find a solution of Stokes flow problems with Dirichlet and Neumann boundary conditions in axisymmetry using an efficient, non-singular, method of fundamental solutions that does not require an artificial boundary, i.e. source points of the fundamental solution coincide with the collocation points on the boundary. The fundamental solution of the Stokes pressure and velocity represents analytical solution of the flow due to a singular Dirac delta source in infinite space. Methodology – Instead of the singular source, a non-singular source with a regularization parameter is employed. Regularized axisymmetric sources were derived from the regularized three-dimensional sources by integrating over the symmetry coordinate. The involved analytical expressions for related Stokes flow pressure and velocity around such regularized axisymmetric sources have been derived. The solution to the problem is sought as a linear combination of the fields due to the regularized sources that coincide with the boundary. The intensities of the sources are chosen in such a way that the solution complies with the boundary conditions. Findings – An axisymmetric driven cavity numerical example, the flow in a hollow tube and the flow between two concentric tubes are chosen to assess the performance of the method. The results of the newly developed method of regularized sources in axisymmetry are compared with the results obtained by the fine-grid second-order classical finite difference method and analytical solution. The results converge with a finer discretization, however, as expected, they depend on the value of the regularization parameter. The method gives accurate results if the value of this parameter scales with the typical nodal distance on the boundary.
COBISS.SI-ID: 1206954
In this paper, the Non-singular Method of Fundamental Solutions (NMFS) is extended to three-dimensional (3D) isotropic linear elasticity problems. In order to avoid the singularities in the classical Method of Fundamental Solutions (MFS), are the source points outside the problem domain replaced by normalizing the volume integral of the fundamental solutions over the sphere around the singularity on the physical boundary. The derivatives of the fundamental solutions at the singularity, required in the traction boundary conditions, are calculated from three reference solutions of the linearly varying simple displacement fields. The artificial boundary appearing in MFS is with this operations removed in NMFS. A comparison between NMFS and MFS solutions and analytical solutions for two single and two bi-material elasticity problems is used to assess the feasibility and the accuracy of the newly developed 3D method. Although NMFS results are slightly less accurate than MFS results in all spectra of performed tests, all NMFS results converge to the analytical solution. The lack of artificial boundary is particularly advantageous when using NMFS in multibody problems. The developments describe a first use of NMFS for 3D solid mechanics problems.
COBISS.SI-ID: 16200475
The purpose of the present paper is the development of meshless diffuse approximate method in connection with the phase field formulation for solution of two-phase flow problems. The numerical approach enables single-domain, fixed-node treatment of the involved moving boundaries. The problem is formulated for Newtonian fluids based on a physical model that involves a coupled set of Navier–Stokes and Cahn–Hilliard equations. Diffuse approximate method is structured with a second order polynomial basis, Gaussian weight function, adaptive upwind scheme and eleven-node local subdomain. The pressure-velocity coupling is performed by the incremental fractional step method and explicit time discretization is used to solve the governing equations. The method is demonstrated in axisymmetry for a problem of two co-flowing immiscible fluids with different material properties that yield dripping or jetting of the core fluid. An assessment of the novel method is carried out based on comparison of the present results with the finite volume method outcome. A sensitivity study of various process parameters is carried out and verified against the previously published results. The paper represents a pioneering development in simulation of two-phase flows by a meshless method.
COBISS.SI-ID: 16111387
Serial femtosecond crystallography requires reliable and efficient delivery of fresh crystals across the beam of an X-ray free-electron laser over the course of an experiment. We introduce a double-flow focusing nozzle to meet this challenge, with significantly reduced sample consumption, while improving jet stability over previous generations of micro-nozzles. We demonstrate its use to determine the first room-temperature structure of RNA polymerase II at high resolution, revealing new structural details. Moreover, the double flow-focusing nozzles were successfully tested with three other protein samples, utilizing the improved operation and characteristics of these devices. Explanation: Slovenian project team has contributed to development of this breaktrough novel micro-nozzle by virtual computational design, based on outcomes of the present project.
COBISS.SI-ID: 1296042
The purpose of this paper is to simulate a macrosegregation solidification benchmark by a meshless diffuse approximate method. The benchmark represents solidification of Al 4.5 wt per cent Cu alloy in a 2D rectangular cavity, cooled at vertical boundaries. A coupled set of mass, momentum, energy and species equations for columnar solidification is considered. The phase fractions are determined from the lever solidification rule. The meshless diffuse approximate method is structured by weighted least squares method with the second-order monomials for trial functions and Gaussian weight functions. The spatial localization is made by overlapping 13-point subdomains. The time-stepping is performed in an explicit way. The pressure-velocity coupling is performed by the fractional step method. The convection stability is achieved by upstream displacement of the weight function and the evaluation point of the convective operators. The results show a very good agreement with the classical finite volume method and the meshless local radial basis function collocation method. The simulations are performed on uniform and non-uniform node arrangements and it is shown that the effect of non-uniformity of the node distribution on the final segregation pattern is almost negligible. The application of the meshless diffuse approximate method to simulation of macrosegregation is performed for the first time. An adaptive upwind scheme is successfully applied to the diffuse approximate method for the first time.
COBISS.SI-ID: 1386922