Development of a high-order finite volume method with multiblock partition techniques

Lemos, E. M.; Secchi, Argimiro Resende; Biscaia, Evaristo C.

doi:10.1590/s0104-66322012000100019

Cited by 3 publications

(1 citation statement)

References 19 publications

(35 reference statements)

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“…Tis interface approximation converts partial diferential equations into a set of algebraic equations. In the past, based on diferent choices to these interface approximations, several numerical techniques of fnite volume method (FVM) formulation are developed [45][46][47][48][49][50]. Te convection-difusion equation can be either convectiondominated or difusion-dominated its depending on the rate of convection and difusion.…”

Section: Introductionmentioning

confidence: 99%

Numerical Approximation of One-Dimensional Transport Model Using an Hybrid Approach in Finite Volume Method

Hussain

Ali

2023

Mathematical Problems in Engineering

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A finite volume method is a well-known and appropriate approach for numerical approximation of governing problems. This article proposes a finite volume approach to simulate the one-dimensional convection–diffusion transport problem. New expressions for interface approximation are constructed by combining the assumption of step-wise profile and piece-wise linear profile. In addition, a new numerical technique is developed based on these new interface approximations. This new numerical algorithm produces consistent results for numerical approximation of the governing problem and gives second-order accuracy along space and time. In order to justify the effectiveness of our numerical technique, numerical experiments are conducted for various magnitudes of convection and diffusion coefficients. The numerical results of the proposed algorithm are also compared to the finite volume method and the finite difference method. Based on this comparison, our numerical scheme presents stable and highly accurate results compared to the alternatives.

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Section: Introductionmentioning

confidence: 99%

Numerical Approximation of One-Dimensional Transport Model Using an Hybrid Approach in Finite Volume Method

Hussain

Ali

2023

Mathematical Problems in Engineering

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Forced Turbulent Convection Along Heated and Cooled Walls With Variable Fluid Properties

Sufrà

Steiner

2021

Journal of Fluids Engineering

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The effect of temperature depending material properties on heat and momentum transfer along heated/cooled walls in turbulent pipe flow was investigated using direct numerical simulations (DNS). For the considered thermal wall conditions, always associated with a molecular Prandtl number well over unity Prw = 10, the significantly dampened/enhanced turbulent motion caused by the increase/decrease of the viscosity with distance to the heated/cooled wall, turned out to clearly dominate over the opposite trend of the enthalpy fluctuations. The Nusselt number and, quantitatively less pronounced, the wall friction coefficient are accordingly decreased/increased for the heated/cooled case. A comparison against a well established Nu-correlation unveils the limits of the generally applied approach, which is essentially based on uniform bulk flow conditions and subsequently modified accounting for material property variation, when applied to heated and cooled conditions. An enhanced disparity of the turbulent normal stresses is observed inside the inertial subrange for the heated case, indicating a stronger deviation from isotropic turbulence, which possibly challenges mostly isotropic standard turbulence models.

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Numerical Analysis of Convection–Diffusion Using a Modified Upwind Approach in the Finite Volume Method

2020

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The main focus of this study was to develop a numerical scheme with new expressions for interface flux approximations based on the upwind approach in the finite volume method. Our new proposed numerical scheme is unconditionally stable with second-order accuracy in both space and time. The method is based on the second-order formulation for the temporal approximation, and an upwind approach of the finite volume method is used for spatial interface approximation. Some numerical experiments have been conducted to illustrate the performance of the new numerical scheme for a convection–diffusion problem. For the phenomena of convection dominance and diffusion dominance, we developed a comparative study of this new upwind finite volume method with an existing upwind form and central difference scheme of the finite volume method. The modified numerical scheme shows highly accurate results as compared to both numerical schemes.

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Development of a high-order finite volume method with multiblock partition techniques

Cited by 3 publications

References 19 publications

Numerical Approximation of One-Dimensional Transport Model Using an Hybrid Approach in Finite Volume Method

Numerical Approximation of One-Dimensional Transport Model Using an Hybrid Approach in Finite Volume Method

Forced Turbulent Convection Along Heated and Cooled Walls With Variable Fluid Properties

Numerical Analysis of Convection–Diffusion Using a Modified Upwind Approach in the Finite Volume Method

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