Solving convection-diffusion-reaction equation by adaptive finite volume element method

Theeraek, P.; Phongthanapanich, Sutthisak; Dechaumphai, Pramote

doi:10.1016/j.matcom.2011.06.002

Cited by 16 publications

(20 citation statements)

References 16 publications

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“…The basic idea of the adaptive meshing technique presented herein is to construct a completely new mesh based on the solution obtained from the previous mesh [11,12]. There are two main steps for generating a new adaptive mesh.…”

Section: Adaptive Meshing Techniquementioning

confidence: 99%

“…Key words: Adaptive mesh, convectively-cooled solid, coupled problems, nodeless variable finite element technique [11,12] is also incorporated to further improve the overall solution accuracy. The technique places small elements in the regions of high solution gradients to capture accurate solution.…”

Section: Introductionmentioning

confidence: 99%

“…An adaptive finite element technique is incorporated to further improve the overall analysis solution accuracy. Several examples are presented to evaluate the performance of the proposed method by comparing the predicted solution with the exact solution and/or the solution from solving the full Navier-Stokes equations.Key words: Adaptive mesh, convectively-cooled solid, coupled problems, nodeless variable finite element technique [11,12] is also incorporated to further improve the overall solution accuracy. The technique places small elements in the regions of high solution gradients to capture accurate solution.…”

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confidence: 99%

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Adaptive nodeless variable finite element method for convectively-cooled solid

Puntimakornkij¹,

Malatip²,

Dechaumphai³

2013

J Eng Technol

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INTRODUCTIONConvectively-cooled solid is a common problem encountered in many engineering applications. Due to the complexity of the problem geometry, the finite element method is normally employed to determine the temperature distribution in both the solid and fluid. The Navier-Stokes equations are normally used to solve for the fluid solution behaviors, such as the flow velocities, pressure, and temperature. The flow analysis often requires a large amount of computational time because of many unknowns per node and the governing differential equations are inherently nonlinear [1][2][3][4]. In addition, the finite element method is preferred for the flow solution as compared to other methods because the necessary information can be transferred directly between the solid and fluid during the coupling analysis.In many cooling applications such as flow in tubes and channels, the fluid analysis may be treated as one-dimensional flow. In this case, the Navier-Stokes equations are reduced to a rather simple equation that can be solved simultaneously with the energy equation of the solid [5,6]. The finite element equations of the fluid can be derived, so that they are coupled directly with the finite element equations of the solid. The coupled equations can be solved simultaneously to obtain the temperature distributions in both the solid and fluid.Solving coupled finite element equations as mentioned above requires that the solid and fluid must have the same discretization along the solid/fluid interface. Adding the actual nodes to increase the solution accuracy may cause difficulty in reconstructing a new finite element mesh. Thus, the nodeless variable approach used for the solid [7-10] is extended to analyze the coupled solid/fluid problem in this paper. The idea is to include the nodeless variables into the conventional finite elements without adding the actual nodes so that the analysis solution accuracy is improved without re-discretizing the solid/ fluid finite element model. In addition, an adaptive meshing An adaptive nodeless variable finite element method for analysis of convectively-cooled solid is presented.The method solves two-dimensional heat transfer in solid coupling with one-dimensional heat transfer of fluid flow in channel. The nodeless variable finite element concept is introduced to increase the solution accuracy without adding the actual nodes. An adaptive finite element technique is incorporated to further improve the overall analysis solution accuracy. Several examples are presented to evaluate the performance of the proposed method by comparing the predicted solution with the exact solution and/or the solution from solving the full Navier-Stokes equations.Key words: Adaptive mesh, convectively-cooled solid, coupled problems, nodeless variable finite element technique [11,12] is also incorporated to further improve the overall solution accuracy. The technique places small elements in the regions of high solution gradients to capture accurate solution. At the same time, larger elements are gene...

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Section: Adaptive Meshing Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Adaptive nodeless variable finite element method for convectively-cooled solid

Puntimakornkij¹,

Malatip²,

Dechaumphai³

2013

J Eng Technol

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“…Implicit time stepping method was adopted in their study. Theeraek et al (2011) used the adaptive meshing technique to solve the unsteady convection-diffusion-reaction equation on 2D unstructured meshes. In their research, FVM was used to discretize the governing equations while FEM was applied to determine the gradient quantities at cell faces.…”

Section: Introductionmentioning

confidence: 99%

A Proposed Damping Coefficient of Quick Adaptive Galerkin Finite Volume Solver for Elasticity Problems

Yazdi¹,

Amiri²,

Gharebaghi³

2019

JSSCM

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A Quick Adaptive Galerkin Finite Volume (QAGFV) solution of Cauchy momentum equations for plane elastic problems is presented in this research. A new damping coefficient is introduced to preserve the efficiency of the iterative pseudo-explicit solution procedure. It is shown that the numerical oscillations are not only effectively damped by the proposed damping coefficient, but also that the rate of the convergence of QAGFV algorithm increases. Furthermore, the numerical results show that the proposed coefficient is not sensitive to the spatial discretization. In order to improve the accuracy of the computed stress and displacement fields, an automatic twodimensional h-adaptive mesh refinement procedure is adopted for shape-function-free solution of the governing equations. For verification, two classical problems and their analytical solutions have been investigated. The first is a uniaxial loaded plate with holes, and the second is a cantilever beam under a concentrated load. The results show a good agreement between QAGFV and analytical method. Moreover, the direct and iterative approaches of the finite element method have been implemented in FORTRAN to evaluate the efficiency and accuracy of the presented algorithm. In the end, the corresponding results of some problems have been compared to the QAGFV solutions. The results confirm that the presented h-adaptive QAGFV solver is accurate and highly efficient especially in a large computational domain.

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“…Theeraek et al [27] used a FVE method incorporating an adaptive meshing technique to solve the 2-D unsteady scalar convection-diffusion equation. They achieved second-order accuracy in both space and time.…”

Section: Introductionmentioning

confidence: 99%

Extending a Hybrid Finite-Volume-Element Method to Solve Laminar Diffusive Flame

Darbandi

Ghafourizadeh

2014

Numerical Heat Transfer, Part B: Fundamentals

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We extend a hybrid finite-volume-element (FVE) method to treat the laminar reacting flow in cylindrical coordinates considering the collocation of all chosen primitive variables. To approximate the advection fluxes at the cell faces, we use the upwind-biased physical influence scheme PIS and derive a few new extended expressions applicable in the cylindrical frame. These expressions are derived for both the Navier-Stokes and reactive flow governing equations, of which the latter expressions are considered novel in the finite-volume formulation. To validate our derived expressions, the current results are compared with the experimental data and other available numerical solutions. The results show that the accuracy of the current expressions is better than those derived by the past similar numerical investigators.

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Solving convection-diffusion-reaction equation by adaptive finite volume element method

Cited by 16 publications

References 16 publications

Adaptive nodeless variable finite element method for convectively-cooled solid

Adaptive nodeless variable finite element method for convectively-cooled solid

A Proposed Damping Coefficient of Quick Adaptive Galerkin Finite Volume Solver for Elasticity Problems

Extending a Hybrid Finite-Volume-Element Method to Solve Laminar Diffusive Flame

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