Numerical Scheme to Simulate Combined Mixing and Separating Newtonian Fluid Flow in a Channel

2013 ◽  
Vol 303-306 ◽  
pp. 2798-2805
Author(s):  
Rahim Bux Khokhar ◽  
Y. K. Chen ◽  
R. K. Calay ◽  
Y Xu
Keyword(s):  
Finite Element ◽  
Fluid Flow ◽  
Numerical Scheme ◽  
Implicit Time ◽  
Finite Element Scheme ◽  
Time Stepping ◽  
The Common ◽  
Flow Directions ◽  
Steady Solutions ◽  
Element Algorithm

The paper presents a semi-implicit time-stepping Taylor-Galerkin pressure correction primitive variable finite element algorithm to simulate fluid flow for two dimensional planar combined mixing and separating geometry. Two cases; one with reversed channel flows interacting through a gap in the common separating walls filled with Newtonian fluids in both arms of the channels and other with unidirectional flows were modeled in order to examine the performance of the scheme. Steady solutions were obtained using unsteady finite element scheme. The influence of increasing inertia on variation in flow directions and varying flow rate configurations in both channel arms are studied in detail. The scheme is found to be fast, robust and stable for varying Reynolds number.

Unconditionally stable numerical scheme for natural convection problems

2014 ◽  
Vol 24 (4) ◽  
pp. 907-919 ◽  
Author(s):  
Bartosz Górecki ◽  
Jacek Szumbarski
Keyword(s):  
Fluid Flow ◽  
Natural Convection ◽  
Numerical Scheme ◽  
Temporal Order ◽  
Mathematical Formulation ◽  
Time Step ◽  
Unconditionally Stable ◽  
Content Type ◽  
Time Step Size ◽  
Time Stepping

Purpose – Both the importance of the natural convection in science and engineering and the shortage of publications in the field of numerical features of time-stepping schemes for the simulation of coupled heat and fluid flow problems motivate the present work. The paper aims to discuss these issues. Design/methodology/approach – The paper presents the unconditionally stable time-stepping scheme for simulation of coupled problems of mass and heat transport. The paper is divided into two parts. The first part concerns the mathematical formulation of the scheme and discusses its implementation. The second part focuses on the numerical simulation and its results. A detailed investigation of the temporal order of the scheme with respect to the L2-norms of the errors of the pressure, velocity, temperature and divergence of velocity fields has also been given. Findings – The work shows that it is possible to formulate a numerical scheme which is unconditionally stable with respect to the time step size. Moreover, application of the spectral element method for the spatial discretization results in a high order of approximation in space and very good overall accuracy. Furthermore, the investigation of the numerical features of the scheme showed that the formal temporal order of the scheme (formally second order) has been deferred very slightly and the order of 1.8-1.9 is achieved for all unknown fields. Originality/value – The paper presents a new unconditionally stable scheme for simulation of unsteady flows with bidirectional coupling of heat transfer and the fluid flow. It also carefully investigates the numerical behaviour of the method.

scholarly journals Modeling of linear dispersive materials using scalable time domain finite element scheme

2016 ◽  
Vol 65 (4) ◽  
pp. 719-732
Author(s):  
Bogusław Butryło
Keyword(s):  
Finite Element ◽  
Time Domain ◽  
Time Dependent ◽  
Dispersive Media ◽  
Benchmark Problem ◽  
The Finite Element Method ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Convolution Integrals ◽  
Element Algorithm

Abstract This paper deals with some aspects of formulation and implementation of a broadband algorithm with build-in analysis of some dispersive media. The construction of the finite element method (FEM) based on direct integration of Maxwell’s equations and solution of some additional convolution integrals is presented. The broadband, fractional model of permittivity is approximated by a set of some relaxation sub-models. The properties of the 3D time-dependent formulation of the FEM algorithm are determined using a benchmark problem with the Cole-Cole and the Davidson-Cole models. Several issues associated with the implementation and some constraints of the broadband finite element algorithm are presented.

scholarly journals Numerical Simulation of Combined Mixing and Separating Flow in Cannel Filled with Porous Media

2013 ◽  
Vol 694-697 ◽  
pp. 639-647
Author(s):  
R. B. Khokhar ◽  
Y. K. Chen ◽  
Y Xu ◽  
R. K. Calay
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Fluid Flows ◽  
Numerical Data ◽  
Newtonian Fluids ◽  
Separating Flow ◽  
Correction Scheme ◽  
Element Approach ◽  
The Common ◽  
Steady Solutions

Various flow bifurcations are investigated for two dimensional combined mixing and separating geometry. These consist of two reversed channel flows interacting through a gap in the common separating wall filled with porous media of Newtonian fluids and other with unidirectional fluid flows. The Steady solutions are obtained through an unsteady finite element approach that employs a Taylor-Galerkin/pressure-correction scheme. The influence of increasing inertia on flow rates are all studied. Close agreement is attained with numerical data in the porous channels for Newtonian fluids. Keywords: mixing-separating geometry, flow bifurcation, porous media, finite element method, Newtonian fluid.

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