Matjaž Ramšak

Mixed boundary elements for laminar flows

We present a mixed boundary element formulation of the boundary domain integral method (BDIM) for solving diffusion-convective transport problems. The basic idea of mixed elements is the use of a continuous interpolation polynomial for conservative field function approximation and a discontinuous interpolation polynomial for its normal derivative along the boundary element. In this way, the advantages of continuous field function approximation are retained and its conservation is preserved while the normal flux values are approximated by interpolation nodal points with a uniquely defined normal direction. Due to the use of mixed boundary elements, the final discretized matrix system is overdetermined and a special solver based on the least squares method is applied. Driven cavity, natural and forced convection in a closed cavity are studied. Driven cavity results at Re = 100, 400 and 1000 agree better with the benchmark solution than Finite Element Method or Finite Volume Method results for the same grid density with 21 × 21 degrees of freedom

Boundary element method for thermal flows using k‐ε turbulence models

Purpose – This paper aims to develop a multidomain boundary element method (BEM) for modeling 2D complex turbulent thermal flow using low Reynolds two‐equation turbulence models.Design/methodology/approach – The integral boundary domain equations are discretised using mixed boundary elements and a multidomain method also known as a subdomain technique. The resulting system matrix is an overdetermined, sparse block banded and solved using a fast iterative linear least squares solver.Findings – The simulation of a turbulent flow over a backward step is in excellent agreement with the finite volume method using the same turbulent model. A grid consisting of over 100,000 elements could be solved in the order of a few minutes using a 3.0 Ghz P4 and 1 GB memory indicating good efficiency.Originality/value – The paper shows, for the first time, that the BEM is applicable to thermal flows using k‐e.

Comparison of Stream‐vorticity and Velocity‐vorticity Formulation of Navier‐Stokes Equations using Multidomain BEM

The paper deals with comparison of two 2D formulations of Navier‐Stokes equations: stream function‐vorticity and its derivation the velocity‐vorticity formulation. The boundary condition for vorticity transport equation is the crucial part. Both sets of governing equations are solved using the same numerical algorithm based on multidomain boundary element method (BEM). Driven cavity flow is the numerical example showing considerable efficiency advantage for stream‐vorticity, while accuracy is practically the same.