Natural convective heat transfer in a fluid saturated variable porosity medium

This article introduces a high-accuracy discrete singular convolution (DSC) for the numerical simulation of coupled convective heat transfer problems. The problem of a buoyancy-driven cavity is solved by two completely independent numerical procedures. One is a quasi-wavelet-based DSC approach, which uses the regularized Shannon's kernel, while the other is a standard form of the Galerkin finite-element method. The integration of the Navier-Stokes and energy equations is performed by employing velocity correction-based schemes. The entire laminar natural convection range of 10 3 h Ra h 10 8 is numerically simulated by both schemes. The reliability and robustness of the present DSC approach is extensively tested and validated by means of grid sensitivity and convergence studies. As a result, a set of new benchmark quality data is presented. The study emphasizes quantitative, rather than qualitative comparisons.

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A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution

In this paper, an artificial compressibility scheme using the finite element method is introduced. 2002 Zienkiewicz Silver Medal and Prize winning paper. The multi-purpose CBS scheme is implemented in its fully explicit form to solve incompressible fluid dynamics problems. It is important to note that the scheme developed here includes split and velocity correction. The proposed method takes advantage of good features from both velocity correction and standard artificial compressibility schemes. Unlike many other artificial compressibility schemes, the proposed one works on a variety of grids and gives results for a wide range of Reynold's numbers. The paper presents some bench mark two- and three-dimensional steady and unsteady incompressible flow solutions obtained from the proposed scheme. Copyright © 2003 John Wiley & Sons, Ltd.

An efficient artificial compressibility (AC) scheme based on the characteristic based split (CBS) method for incompressible flows

https://ntrs.nasa.gov/api/citations/19930013636/downloads/19930013636.pdf

Large-scale computation of incompressible viscous flow by least-squares finite element method

Direct numerical simulation of three-dimensional flow past a yawed circular cylinder of infinite length

A comparative investigation, based on a series of numerical tests, of two purely explicit and one semi-implicit finite element methods used for incompressible flow computation is presented. The ‘segregated’ approach is followed and the equations of motion are considered sequentially. The fundamental concepts and characteristics of the formulations and the solution methodology used are described in technical detail. Various modifications to Chorin's projection algorithm are investigated, particularly with respect to their effects on stability and accuracy. The stability of the semi-implicit method is shown to be less restrictive when compared to the explicit methods as the Reynolds number increases. At large time steps the artificial viscosity is also reduced and higher accuracy is obtained. The performance of the methods discussed in this paper is illustrated by the numerical solutions obtained for the cavity flow and flow past a rearward-facing step problems at high Reynolds numbers, and free convection flow problem at high Rayleigh numbers. It is shown that the semi-implicit method needs fewer iterations than the explicit methods, and the accuracy of the present methods is guaranteed by comparison with the existing methods.

Semi‐implicit and explicit finite element schemes for coupled fluid/thermal problems

A numerical procedure for solving the time-dependent, incompressible Navier–Stokes and energy equations is presented. The present method is based on a set of finite element equations of the primitive variable formulation, and a time-splitting procedure which has unique features in its formulation as well as in its evaluation from the viewpoint of efficiency and accuracy. The applicability of the proposed formulation was verified by computations and comparison with known results.

Some recent trends and developments in finite element analysis for incompressible thermal flows

Hydraulic jump on a straight horizontal channel with supercritical Froude numbers 2·0 and 4·0 is numerically simulated by solving the Reynolds averaged Navier–Stokes equations. Turbulence is modelled through the k–ϵ closure equations and the mixed Eulerian–Lagrangian description of flow is utilized to overcome the problem posed by moving free boundary. Time stepping is done via fractional step method and pressure is determined from Poisson's equation. Galerkin finite element method with three-noded triangular elements is used for spatial discretization. A detailed study of the internal and external characteristics of hydraulic jump is done and compared with experimental values where possible. Surface roller and recirculation zone are found to play a dominant role in turbulence generation and dissipation.

Numerical simulation of hydraulic jump

In this work, a semi-implicit projection-type finite element method is applied to solve the incompressible oscillatory cavity flow with heat transfer. The two-dimensional, time-dependent Navier-Stokes and energy equations are numerically integrated by a time-split Galerkin finite element method using direct matrix solvers. The time accuracy of the method was tested by calculating the transient buoyancy-driven flow in a square cavity with differentially heated vertical walls. The oscillatory cavity flow is then studied considering the effects of heat transfer, Reynolds number, and oscillatory Stokes number to measure the stability of the scheme for such a high singularity phenomenon. The proposed scheme is found to be stable and convergent for high Rayleigh numbers, and will be applicable to general problems involving flow and heat transfer, especially in three dimensions.

Finite Element Analysis of Oscillatory Flow with Heat Transfer Inside a Square Cavity

This paper reports on the development of a semi-implicit projection-type scheme for solving incompressible Navier-Stokes and energy equations. The numerical scheme employs a finite-element method using a time-splitting method to integrate the two-dimensional full Navier-Stokes and energy equations satisfying continuity constraints to machine accuracy. The fundamental concepts and characteristics of the formulations and the solution methodology used are described in detail. The performance of the method is illustrated by numerical solutions obtained for two-dimensional fluid flows in a square cavity with an impulsively starting lid and with an oscillating lid, considering the effects of heat transfer, Reynolds number, Rayleigh number, and oscillatory Stokes number. The results are compared with those available in the literature and are based on alternative approaches to treat incompressibility and convective acceleration.

B. Ramaswamy

Papers

Semi‐implicit and explicit finite element schemes for coupled fluid/thermal problems

Some recent trends and developments in finite element analysis for incompressible thermal flows

Numerical simulation of hydraulic jump

Finite Element Analysis of Oscillatory Flow with Heat Transfer Inside a Square Cavity

Finite-Element Analysis of Unsteady Two-Dimensional Navier-Stokes Equations