The purpose of this paper is to present the solution of a highly nonlinear fluid dynamics in a low Prandtl number regime, typical for metal-like materials, as defined in the call for contributions to a numerical benchmark problem for 2D columnar solidification of binary alloys. The solution of such a numerical situation represents the first step towards understanding the instabilities in a more complex case of macrosegregation. The involved temperature, velocity and pressure fields are represented through the local approximation functions which are used to evaluate the partial differential operators. The temporal discretization is performed through explicit time stepping. The performance of the method is assessed on the natural convection in a closed rectangular cavity filled with a low Prandtl fluid. Two cases are considered, one with steady state and another with oscillatory solution. It is shown that the proposed solution procedure, despite its simplicity, provides stable and convergent results with excellent computational performance. The results show good agreement with the results of the classical finite volume method and spectral finite element method. The solution procedure is formulated completely through local computational operations. Besides local numerical method, the pressure correction is performed locally also, retaining the correct temporal transient. Comment: published invited keynote lecture.
B.04 Guest lecture
COBISS.SI-ID: 2599419We make an overview of our achievements in the development of meshless local radial basis function collocation method for solids and fluids. We describe the use of the method in termomechanical processing of steel and aluminium alloys. Comment: Taiyuan University of Technology and University of Nova Gorica have after the lecture signed a written collaboration contract.
B.05 Guest lecturer at an institute/university
COBISS.SI-ID: 3031547The purpose of the present paper is development of a Non-singular Method of Fundamental Solutions (NMFS) for Stokes flow problems, widely applicable in biomedical engineering. The NMFS is based on the classical Method of Fundamental Solutions (MFS) with regularization of the singularities. The Stokes problem is decomposed into three coupled Laplace problems. The solution is structured by collocating the pressure and the velocity field boundary conditions by the Laplace fundamental solution. The regularization is achieved by replacement of the concentrated point sources by distributed sources over the disks around the singularity of fundamental solution. The NMFS solution is compared to MFS solution and analytical solution (a.s.) in case of simple 2D duct flow. The described developments represent a first use of NMFS for Stokes problems. The method requires the discretization on the boundary only and is easily applicable in 3D, thus representing an ideal candidate for solving complex biomedical engineering free and moving boundary flow problems in the future.
F.02 Acquisition of new scientific knowledge
COBISS.SI-ID: 3041019