New hybrid compact schemes for structured irregular meshes using Birkhoff polynomial basis

Maurya, Praveen Kumar; Rajpoot, Manoj K.; Yadav, Vivek S.; Singh, Ankit

doi:10.1016/j.jcp.2020.109808

Cited by 2 publications

(3 citation statements)

References 48 publications

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“…k [2] eq Û(k, t)e ikx j dk (14) where k [i] eq , i = 1, 2 are the equivalent wave numbers for first-and second-order spatial derivatives, respectively, and ±k m are provided by the Nyquist limit. For the spectral analysis, compact schemes can be represented using matrix notations.…”

Section: Global Spectral Analysismentioning

confidence: 99%

“…Compact schemes on non‐uniform grids are given in References 8‐14. developed compact schemes on non‐uniform grids also.…”

Section: Introductionmentioning

confidence: 99%

“…Shukla and Zhong in Reference 15 used polynomial interpolation to derive the compact schemes for non‐uniform grids for the first and second‐order derivatives on a collocated grid. Sengupta and Sengupta 16 and Maurya et al 14 also developed the compact schemes on non‐uniform grid using biased stencils. For the simulation of compressible flow, Gamet et al 17 formulated compact difference schemes for first‐ and second‐order derivatives on non‐uniform grids in which the coefficient matrix for derivative is identical to their value for uniform grid‐spacing case 18 .…”

Section: Introductionmentioning

confidence: 99%

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New compact difference schemes on non‐uniform collocated and staggered grids for convection‐dominated flows

Yadav

Maurya²,

Rajpoot

2022

Numerical Methods in Fluids

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Summary This paper deals with the formulation of the tridiagonal compact difference schemes for derivatives up to second‐order with boundary stencils on non‐uniform grids. A compact scheme for the first derivative with interpolation is also devised on staggered non‐uniform grids. The developed schemes with non‐uniform spacing transform to respective classical compact schemes for the case of uniform mesh spacing. The resolution, numerical diffusion, and anti‐diffusion features of the devised schemes are evaluated using global spectral analysis. Applications to the direct numerical simulation (DNS) of two‐dimensional lid‐driven cavity (LDC) flow governed by Navier‐Stokes equations and wave‐propagation following linear rotating shallow water (LRSWE) equations with variable grid‐spacing are discussed at different choices of parameters. Computed results are also compared with solutions available in the literature.

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Section: Global Spectral Analysismentioning

confidence: 99%

“…Compact schemes on non‐uniform grids are given in References 8‐14. developed compact schemes on non‐uniform grids also.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New compact difference schemes on non‐uniform collocated and staggered grids for convection‐dominated flows

Yadav

Maurya²,

Rajpoot

2022

Numerical Methods in Fluids

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Novel hybrid compact schemes for stream function–velocity formulation of the incompressible Navier–Stokes equations

Yadav

Maurya

Maurya³

et al. 2023

Physics of Fluids

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In this paper, we have developed new hybrid compact schemes for the simulation of stream function-velocity formulation of the two-dimensional incompressible Navier-Stokes equation. The first-order spatial derivatives are approximated by the optimized upwind compact scheme, and the Laplacian and biharmonic operators are discretized using fourth-order hybrid compact schemes. Moreover, we have also performed Fourier analysis to assess the resolution and added numerical diffusion properties of numerical schemes for stream function-velocity formulation of the linear Navier-Stokes equation. For time discretization, we have used explicit fourth-stage fourth-order Runge-Kutta method and hybrid filters. Furthermore, to validate the accuracy and efficiency of the schemes, several fluid flow problems, including a test problem with a non-homogeneous source term and a lid-driven cavity problem, are considered. Numerical results exhibit a great match to the results reported in the literature at lower computational cost with hybrid filters.

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New hybrid compact schemes for structured irregular meshes using Birkhoff polynomial basis

Cited by 2 publications

References 48 publications

New compact difference schemes on non‐uniform collocated and staggered grids for convection‐dominated flows

New compact difference schemes on non‐uniform collocated and staggered grids for convection‐dominated flows

Novel hybrid compact schemes for stream function–velocity formulation of the incompressible Navier–Stokes equations

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