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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 H 2 -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 H 2 -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. [ABSTRACT FROM AUTHOR]

In this paper, we couple a numerical method aimed at simulation of flow and heat transfer of nanofluids with stochastic modelling of input and material parameters. In order to simulate nanofluids, an in-house numerical method was developed, based on the solution of 3D velocity–vorticity formulation of Navier–Stokes equations. A fast Boundary-Domain Integral Method has been employed to solve the governing equations and set up the deterministic flow and heat transfer solver. The developed algorithm is used to simulate natural convection of a nanofluid in a closed cavity. The uncertainty present in the input parameters is propagated to the output of interest via the Stochastic Collocation Method. The stochastic mean, variance, and higher-order moments of the output values are presented. The non-intrusive nature of the Stochastic Collocation Method facilitates the previously validated deterministic code to remain unchanged. The stochastic analysis reveals that the uncertainty of input parameters influences the output results most in the areas where high flow field gradients appear. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we present a method to decrease the computational cost of the Boundary-Domain Integral Method. We focus on the solution of the velocity–vorticity formulation of the Navier–Stokes equation for incompressible 3D fluid flow. The objective is to accelerate the solution of the boundary vorticity values. In order to reduce the computational cost of the Boundary-Domain Integral Method, we employ the Adaptive Cross Approximation algorithm in combination with the hierarchical matrix structure. The hierarchical matrix structure enables higher compression rates when individual matrix parts are approximated by low-rank matrices. We use the fundamental solution of the modified Helmholtz equation to improve further the approximation accuracy when solving the boundary vorticity values. The developed algorithm is used to simulate natural convection in a closed cavity. By comparing the simulation results with a published benchmark, we are able to assess the influence of the approximation techniques and give a recommendation on parameter values that lead to optimal compression characteristics when simulating the heat and mass transfer processes. [ABSTRACT FROM AUTHOR]

Abstract: A wavelet transform based BEM numerical scheme is used for Large Eddy Simulation of turbulent natural and forced convection of air flowing over a solar thermal collector. The collector is enclosed by vertical fins forming an open shallow cavity. The numerical scheme employs the velocity–vorticity formulation of Navier–Stokes equations using LES turbulence model where boundary element and finite element methods are combined. Grids with up to 2×105 nodes are used in simulations lasting for 6×104 time steps. Three inflow air velocities are considered corresponding to Reynolds number value up to . Temperature difference between air and collector of about 50K is considered. Heat transfer from the thermal solar collector is studied via the average Nusselt number value, its time series and its relationship to the values of Reynolds and Rayleigh numbers. The results show that the largest heat losses occur behind the fin due to shedding of large vortices that transport hot air away from the collector. Heat losses decrease along the central part of the collector and feature another smaller peak just before the air hits the fin on the opposite side of the collector. [Copyright &y& Elsevier]

Abstract: In this paper we analyse flow and heat transfer characteristics of nanofluids in natural convection flows in closed cavities. We consider two test cases: natural convection in a three-dimensional differentially heated cavity, and flow around a hotstrip located in two positions within a cavity. Simulations were performed for Rayleigh number values ranging from 103 to 106. Performance of three types of water based nanofluids was compared with pure water and air. Stable suspensions of Cu, Al2O3 and TiO2 solid nanoparticles in water were considered for different volume fractions ranging up to 20%. We present and compare heat flux for all cases and analyse heat transfer enhancement attributed to nanofluids in terms of their enhanced thermal properties and changed flow characteristics. Results show that, using nanofluids, the largest heat transfer enhancements can be achieved in conduction dominated flows as well as that nanofluids increase the three-dimensional character of the flow field. We additionally examine the relationship between vorticity, vorticity flux and heat transfer for flow of nanofluids. The simulations were performed using a three-dimensional boundary element method based flow solver, which has been adapted for the simulation of nanofluids. The numerical algorithm is based on the combination of single domain and subdomain boundary element method, which are used to solve the velocity–vorticity formulation of Navier–Stokes equations. In the paper we present the adaptation of the solver for simulation of nanofluids. Additionally, we developed a dynamic solver accuracy algorithm, which was used to speed up the simulations. [ABSTRACT FROM AUTHOR]

We propose a novel approach for two-way coupled simulations of multiphase flows within an Eulerian-Lagrange framework. Lagrangian particles are commonly approximated as point sources of either energy, mass or momentum. To introduce them into the Eulerian computation of the fluid flow, an approximation of the Dirac delta function has to be made. By resorting to the Boundary Element Method (BEM) based computation of fluid flow, it is possible to implement the point source concept without any numerical approximation by simply taking advantage of the properties of the fundamental solution present in BEM. However, singularity issues occur in the close vicinity of the mesh nodes. To remedy this effect, the particle-in-cell (PIC) method is used. We present a novel hybrid BEM-PIC two-way coupling algorithm and show that the proposed BEM-PIC model gives superior results compared to a standard PIC implementation. We introduce a critical distance to separate the domain, where the BEM model can be used and the domain, where the PIC model should be used. The results show that the BEM model can be used in about 97 % − 99 % of the domain depending on the mesh used. We provide a criterion for estimating the critical distance within the novel hybrid BEM-PIC two-way coupling algorithm. [ABSTRACT FROM AUTHOR]

Abstract The objective of this article is to develop a boundary element numerical model to solve coupled problems involving heat energy diffusion, convection and radiation in a participating medium. Radiation is modelled using two approaches for optically thick fluids: the Rosseland diffusion approximation and the P 1 approximation. The governing Navier–Stokes equations are written in the velocity–vorticity formulation for the kinematics and kinetics of the fluid motion. The approximate numerical solution algorithm is based on boundary element numerical model in its macro-element formulation. The developed algorithm is validated by comparing results of radiative heat transfer for different optical thicknesses with benchmark data. Furthermore, the developed algorithm is tested by simulating natural convection and radiation heat transfer under large temperature differences where compressible flow solution is required. [ABSTRACT FROM AUTHOR]