Nodal Integral Method Using Quadrilateral Elements for Transport Equations: Part 2-Navier-Stokes Equations

Kumar, Neeraj; Singh, Suneet; Doshi, J. B.

doi:10.1080/10407790.2013.784124

Cited by 12 publications

(2 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

See 1 more Smart Citation

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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%