Nodal integral method for 3D time-dependent anisotropic convection-diffusion equation

Jarrah, Ibrahim; Rizwan-uddin,

doi:10.1016/j.anucene.2021.108550

Cited by 9 publications

(5 citation statements)

References 36 publications

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“…Interested readers might find some of the most current NIM advancements for various fluid flow problems. [20][21][22][23][24][25][26][27][28][29] TIP is the primary step in all nodal-based approaches that convert the PDE into a set of approximate ODEs. These ODEs are then solved analytically within a node.…”

Section: Introductionmentioning

confidence: 99%

“…20,30 Recently, significant advances in NIM for irregular geometries have been made to solve various fluid flow problems using algebraic transformations. 21,22,[31][32] Another limitation, which is the main focus of the present study, is that the general use of NIM is restricted only to linear or weakly nonlinear problems because only Picard-based solvers have been used so far for the solution of the NIM scheme. Since Picard-based solvers can only have linear convergence, these solvers cannot unlock the full potential of the scheme.…”

Section: Introductionmentioning

confidence: 99%

“…It was realized that although M 2 NIM gives faster convergence, it compromises the accuracy of the solution. Interested readers might find some of the most current NIM advancements for various fluid flow problems 20–29 …”

Section: Introductionmentioning

confidence: 99%

“…Earlier, NIM schemes coupled with FDM or FEM have been developed to overcome these limitations 20,30 . Recently, significant advances in NIM for irregular geometries have been made to solve various fluid flow problems using algebraic transformations 21,22,31–32 …”

Section: Introductionmentioning

confidence: 99%

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Physics‐based preconditioning of Jacobian‐free Newton–Krylov solver for Navier–Stokes equations using nodal integral method

Ahmed,

Singh,

Kumar

2023

Numerical Methods in Fluids

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The nodal integral methods (NIMs) have found widespread use in the nuclear industry for neutron transport problems due to their high accuracy. However, despite considerable development, these methods have limited acceptability among the fluid flow community. One major drawback of these methods is the lack of robust and efficient nonlinear solvers for the algebraic equations resulting from discretization. Since its inception, several modifications have been made to make NIMs more agile, efficient, and accurate. Modified nodal integral method (MNIM) and modified MNIM (M2NIM) are the two most recent and efficient versions of the NIM for fluid flow problems. M2NIM modifies the MNIM by replacing the current time convective velocity with the previous time convective velocity, leading to faster convergence albeit with reduced accuracy. This work proposes a preconditioned Jacobian‐free Newton–Krylov approach for solving the Navier–Stokes equation using MNIM. The Krylov solvers do not generally work well without an appropriate preconditioner. Therefore, M2NIM is used here as a preconditioner to accelerate the solution of MNIM. Due to pressure–velocity coupling in the Navier–Stokes equation, developing a quality preconditioner for these equations needs significant effort. The momentum equation is solved using the time‐splitting alternate direction implicit method. The velocities obtained from the solution are then used to solve the pressure Poisson equation. The computational results for the Navier–Stokes equation are presented to underscore the advantages of the developed algorithm.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Physics‐based preconditioning of Jacobian‐free Newton–Krylov solver for Navier–Stokes equations using nodal integral method

Ahmed,

Singh,

Kumar

2023

Numerical Methods in Fluids

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“…The nodal method is developed to find precise solutions on relatively coarse meshes of complex geometries. The development of the nodal method introduces the use of node average flow that allows direct coupling with the centered schemes on the mesh and the elaboration in a simplified way of the conventional schemes for temporal walks [40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of the Heat Generated through an Evaporator-Absorber Accompanied by Thermal Storage for the Solar Energy Applications

Latrache

Hammouch

Lamnaouar

et al. 2023

JERA

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An evaporator-absorber geometry allows the absorption of incident solar radiation andconverts it into thermal energy useful for the evaporation of a working fluid. The evaporator-absorberworks with two fluids: a heat transfer fluid transmitting heat to a working fluid, which, circulatesalong the thermal circuit composed of an evaporator, a turbine, a condenser and a pump. The aim ofthis research work is to analyze the heat transfer through the evaporator-absorber and to extract themathematical equations model the heat exchange process between the component elements of theevaporator-absorber: a serpentine tube, a working fluid and a cylindrical tube. In this case, theworking fluid is water, and the heat transfer fluid is air, which is heated by the thermal energyconverted from solar energy. The mathematical equations describing the heat transfer are extractedby using the nodal method and discretized by the finite difference method. Afterwards, the presentwork estimates the outlet temperature of each element of the evaporator-absorber and studies thestorage capacity of the cylindrical tube. Then, the water temperature distribution on the geometry ofthe evaporator and the required quantity of water and the number of spires to have a high outlettemperature of the water vapor are determined. As a result, the mathematical modeling estimated thatthe outlet temperature of the serpentine tube is higher than the outlet temperature of the water.Additionally, the temperature of the storage tube maintains its increase throughout the day. Thequality of the heat transfer in the serpentine tube is improved by placing the tube in a vertical positionand by adopting a lower volume of water compared to the maximum volume, which is supported bythis tube.

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Nodal integral method to solve the two-dimensional, time-dependent, incompressible Navier-Stokes equations in curvilinear coordinates

Jarrah,

Rizwan–uddin

2024

Computers & Mathematics with Applications

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Nodal integral method for 3D time-dependent anisotropic convection-diffusion equation

Cited by 9 publications

References 36 publications

Physics‐based preconditioning of Jacobian‐free Newton–Krylov solver for Navier–Stokes equations using nodal integral method

Physics‐based preconditioning of Jacobian‐free Newton–Krylov solver for Navier–Stokes equations using nodal integral method

Mathematical Modeling of the Heat Generated through an Evaporator-Absorber Accompanied by Thermal Storage for the Solar Energy Applications

Nodal integral method to solve the two-dimensional, time-dependent, incompressible Navier-Stokes equations in curvilinear coordinates

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