A super-compact higher order scheme for the unsteady 3D incompressible viscous flows

Kalita, Jiten C.

doi:10.1007/s40314-013-0090-y

Cited by 11 publications

(6 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…the scheme (41) provides fourth-order accurate solution values on the quasi-variable mesh topology. We observed that the new scheme's theoretical order (41) remains unchanged even if uniform mesh steps are considered. For the computer implementation of the numerical scheme (41), we shall use the Newton-Raphson method for nonlinear problems and the ADI method for linear equations, as described in the subsequent section.…”

Section: ˆ[ )] (mentioning

confidence: 88%

“…The initial and boundary values associated with (42) are the same as defined in (2)-( 5). The application of the compact scheme (41) to the linear ADE (42) in terms of compact operator form results in , , ,…”

Section: Ade and Adi Methodsmentioning

confidence: 99%

“…The scheme (54) solves the ADE (42) with the same magnitude of truncation error obtained in the scheme (41). Now, it is easy to write (54) as an ADI form in the following manner:…”

Section: Ade and Adi Methodsmentioning

confidence: 99%

“…Subsequently, [39,40] reported solutions to the 2D Burger's equation. The three-dimensional coupled Burger's equations were discussed in recent years in [41,42]. The equations are…”

Section: Coupled Burger's Equation and Stability Analysismentioning

confidence: 99%

See 3 more Smart Citations

Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

Jha

Lin

2022

Research Reports on Computer Science

View full text Add to dashboard Cite

A two-level implicit compact formulation with quasi-variable meshes is reported for solving three-dimensions second-order nonlinear parabolic partial differential equations. The new nineteen-point compact scheme exhibit fourth and second-order accuracy in space and time on a variable mesh steps and uniformly spaced mesh points. We have also developed an operator-splitting technique to implement the alternating direction implicit (ADI) scheme for computing the 3D advection-diffusion equation. Thomas algorithm computes each tri-diagonal matrix that arises from ADI steps in minimal computing time. The operator-splitting form is unconditionally stable. The improved accuracy is achieved at a lower cost of computation and storage because the spatial mesh parameters tune the mesh location according to solution values' behavior. The new method is successfully applied to the Navier-Stokes equation, advection-diffusion equation, and Burger's equation for the computational illustrations that corroborate the order, accuracies, and robustness of the new high-order implicit compact scheme. The main highlight of the present work lies in obtaining a fourth-order scheme on a quasi-variable mesh network, and its superiority over the comparable uniform meshes high-order compact scheme.

show abstract

Section: ˆ[ )] (mentioning

confidence: 88%

Section: Ade and Adi Methodsmentioning

confidence: 99%

“…The scheme (54) solves the ADE (42) with the same magnitude of truncation error obtained in the scheme (41). Now, it is easy to write (54) as an ADI form in the following manner:…”

Section: Ade and Adi Methodsmentioning

confidence: 99%

“…Subsequently, [39,40] reported solutions to the 2D Burger's equation. The three-dimensional coupled Burger's equations were discussed in recent years in [41,42]. The equations are…”

Section: Coupled Burger's Equation and Stability Analysismentioning

confidence: 99%

See 2 more Smart Citations

Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

Jha

Lin

2022

Research Reports on Computer Science

View full text Add to dashboard Cite

show abstract

“…Over the years, the application of HOC schemes to computing incompressible viscous flows has gained popularity because of their simplicity, accuracy, and advantages associated with compact stencils. [36][37][38][39][40][41][42][43][44][45][46][47][48][49] To the best of our knowledge only Kalita and Dass 31 have applied an HOC scheme to numerically investigate DDNC in a vertical porous annulus. Previous studies for various cylindrical configurations 8,9,27,28,31 have shown the appearance of thermal and solutal boundary layers in regions (especially near the walls) with steep gradients in temperature and concentration, especially for slender cavities (A 1 ≫ ).…”

Section: Introductionmentioning

confidence: 99%

Heat and mass transfer characteristics of double‐diffusive natural convection in a porous annulus: A higher‐order compact approach

Dutta

Kalita

2021

Heat Trans

Self Cite

View full text Add to dashboard Cite

In this paper, we apply a reconstructed higher-order compact scheme on nonuniform grids to the problem of double-diffusive natural convection in a vertical porous annulus. The Darcy model is adopted for the fluid flow h c h c ). Furthermore, the top and bottom boundaries of the cavity are adiabatic and impermeable.The following assumptions hold for this study:(i) Darcy's law is applicable in the porous medium.(ii) The porous matrix is uniform and in equilibrium with the fluid.

show abstract

Topology of corner vortices in the lid-driven cavity flow: 2D vis a vis 3D

Biswas

Kalita

2020

Arch Appl Mech

View full text Add to dashboard Cite

A super-compact higher order scheme for the unsteady 3D incompressible viscous flows

Cited by 11 publications

References 45 publications

Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

Heat and mass transfer characteristics of double‐diffusive natural convection in a porous annulus: A higher‐order compact approach

Topology of corner vortices in the lid-driven cavity flow: 2D vis a vis 3D

Contact Info

Product

Resources

About