A numerical study of double-diffusive natural convection in porous media using the Boundary Element Method is presented. The studied configuration is a horizontal layer filled with fluid saturated porous media, where different temperature and concentration values are applied on the horizontal walls, while the vertical walls are adiabatic and impermeable. Transport phenomena in porous media are described with the use of modified Navier-Stokes equations in the form of conservation laws for mass, momentum, energy and species. The results for different governing parameters (Rayleigh number, Darcy number, buoyancy ratio and Lewis number) are presented and compared with those in published studies.
In this paper a Boundary Element Method based numerical algorithm is presented for the simulation of three-dimensional unsteady fluid flow and heat transfer. Four different time discretization techniques are considered and compared on a model unsteady heat diffusion problem. Analytical solution of the problem is used to designate the three point second-order finite different approximation of the accumulation term of the transport equations as the most accurate. This choice is incorporated into the flow solver and the developed algorithm is used to simulate Rayleigh-Bénard convection. Oscillatory and chaotic behaviour of the flow field and heat transfer are observed. Temperature slices and velocity vectors are presented. Heat flux is presented in terms of the Nusselt number.
Flow of an incompressible viscous fluid is considered. The velocity-vorticity formulation of the Navier-Stokes equations is used. The kinematics equation is solved for boundary vorticity values using the Boit-Savart law. Solution of the kinetics equation for the domain values is obtained by employing a macro element approach. Using macro elements enables simulations on dense meshes, since it substantially reduces the algorithm's memory requirements.The developed numerical algorithm has been used to simulate laminar flow over a square cylinder in channel. Low Reynolds number steady state flow simulation as well as transient simulation at higher Reynolds numbers has been investigated. The results have been analysed in terms of velocity, vorticity and pressure field distributions in the wake of the cylinder.
In this paper we focus on oscillation and instability of the solution of the convective-diffusive equation depending on the Peclet number. For that purpose, different types of mesh elements and shape functions have been used. For the stabilization of the solution of the convective-diffusive equation for high Peclet numbers, we employed high-order polynomial shape functions, namely residualfree bubble functions. The numerical scheme is based on BEM. For solving the linear homogeneous part of the partial differential equation, the Laplace fundamental solution has been used.We compared quadratic nine-node domain element using Lagrangian shape functions, linear four-node domain element using Lagrangian shape functions and linear four-node domain element using fourth-order bubble enriched functions. Numerical results obtained with linear Lagrangian shape function and bubble enriched functions are compared with the analytical solution.Residual-free bubble functions add stability to simulation and despite the fact that less nodes are used in the domain element, the results are comparable and in some cases even better than the quadratic nine-node domain element. The boundary element method with usage of bubble-enriched functions can resolve problems of convective-diffusion and obtain stable and accurate solutions for this type of governing equations, which are being represented in several types of transport phenomena.
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