An efficient transient Navier–Stokes solver on compact nonuniform space grids

Kalita, Jiten C.; Dass, Anoop K.; Nidhi, Nimisha

doi:10.1016/j.cam.2007.02.021

Cited by 23 publications

(23 citation statements)

References 27 publications

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“…Substituting equations (13), (14) into equation (10) we obtain the following approximation to (9) ( ) …”

Section: Wallmentioning

confidence: 99%

“…Such approximation provides a better representation at shorter length scales and is well applicable for the simulation of waves with high frequency. The application of compact scheme for various fluid flow problems can be obtained from the investigations [1][2][3][4][5][6][7][8][9][10]. Navon and Riphagen [1] developed compact fourth order algorithm by using alternating-direction implicit finite-difference scheme to solve non-linear shallow-water equations, expressed in conservationlaw form.…”

Section: Introductionmentioning

confidence: 99%

“…Li and Tang [6] extended the previous work of Li et al [11] for steady Navier-Stokes equation to unsteady case by using fourth order accurate compact scheme. Kalita et al [7,9] proposed a transformation-free HOC for steady convectivediffusion equation and an efficient transient Navier-Stokes solver by using non-uniform grids. Pandit et al [8] proposed an implicit HOC finite-difference scheme for two-dimensional unsteady Navier-Stokes equations in irregular geometries by using orthogonal grids.…”

Section: Introductionmentioning

confidence: 99%

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Modeling of Shallow-Water Equations by Using Implicit Higher-Order Compact Scheme with Application to Dam-Break Problem

Bagheri¹,

Das²

2013

J Appl Computat Math

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The paper deals with the unsteady two-dimensional (2D) non-linear shallow-water equations (SWE) in conservation-law form to capture the fluid flow in transition. Numerical simulations of dam-break flood wave in channel transitions have been performed for inviscid and incompressible flow by using two new implicit higher-order compact (HOC) schemes. The algorithm is second order accurate in time and fourth order accurate in space, on the nine-point stencil using third order non-centered difference at the wall boundaries. To solve the algebraic system, bi-conjugate gradient stabilized method (BiCGStab) with preconditioning has been employed. Although, both the schemes are able to capture both transient and steady state solution of shallow water equations, the scheme expressed in conservative law form is unconditionally stable. The model results have been validated for dam-break problem and compared with the experimental data for dry and wet bed conditions. The model results are found to be in good agreement with the experimental observations. The proposed scheme is useful to solve to capture flow transition with minimal number of nodal points, particularly for hyperbolic system.

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“…Substituting equations (13), (14) into equation (10) we obtain the following approximation to (9) ( ) …”

Section: Wallmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling of Shallow-Water Equations by Using Implicit Higher-Order Compact Scheme with Application to Dam-Break Problem

Bagheri¹,

Das²

2013

J Appl Computat Math

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“…Much research has focused on formulating efficient numerical schemes to solve Navier-Stokes equations, such as the recent work by Kalita et al [1] and by He and Wang [2]. However, the computational costs are still high for handling accurate numerical simulations except for simple problems in engineering limited to small scale.…”

Section: Introductionmentioning

confidence: 99%

On a special class of analytical solutions to the three-dimensional incompressible Navier–Stokes equations

Nugroho

Ali

Karim

2009

Applied Mathematics Letters

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a b s t r a c tThe three-dimensional incompressible Navier-Stokes equations with the continuity equation are solved analytically in this work. The spatial and temporal coordinates are transformed into a single coordinate ξ . The solution is proposed to be in the form V = ∇Φ + ∇ × Φ where Φ is a potential function that is defined as Φ = P(x, ξ )R(ξ ). The potential function is firstly substituted into the continuity equation to produce the solution for R and the resultant expression is used sequentially in the Navier-Stokes equations to reduce the problem to the class of nonlinear ordinary differential equations in P terms. Here, more general solutions are also obtained based on the particular solutions of P. Explicit analytical solutions are found to be mathematically similar for the cases of zero and constant pressure gradient. Two examples are given to illustrate the applicability of the method. It is also concluded that the selection of variables for the potential function can be interchanged from the beginning, resulting in similar explicit solutions.

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“…New methods are coming up every day for numerically solving the Navier-Stokes equations that govern the kind of flows mentioned above. Of these, the higher-order compact (HOC) finite difference schemes for the computation of incompressible viscous flows (Gupta 1984(Gupta , 1991Kalita et al 2002Kalita et al , 2004Kalita et al , 2008Kalita and Ray 2009;Li et al 1995;Mackinnon and Johnson 1991;Ray and Kalita 2010;Carey 1995, 1998;Strikwerda 1997) are gradually gaining popularity because of their high accuracy and advantages associated with compact difference stencils. These schemes were basically developed for tackling convection-diffusion equations.…”

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confidence: 99%

Higher-order-compact simulation of unsteady flow past a rotating cylinder at moderate Reynolds numbers

Ray

Kalita

2014

Comp. Appl. Math.

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A recently developed transformation-free higher-order compact finite difference scheme, in non-uniform cylindrical polar grids, is extended and applied to study the temporal development of two-dimensional viscous incompressible flow past a circular cylinder which starts translating and rotating impulsively from rest, for two moderate Reynolds numbers (Re) for the rotational parameter α lying between 0.5 and 3. This scheme does not require transformation from the actual flow domain to the computational domain. The scheme is at least third-order accurate in space and second-order accurate in time. To compute the flow, streamfunction-vorticity (ψ-ω) formulation for the two-dimensional Navier-Stokes equations in polar coordinates is used. The drag and lift coefficients along with various other properties related to stream function and vorticity behavior are investigated. The computed results using present scheme for two (Re = 500, Re = 1,000) Reynolds numbers with different rotational parameters are compared with existing experimental and numerical results. Excellent agreement is obtained in all the cases, and in most of the cases, our numerical results are closer to the experimental ones than previously published numerical results.

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An efficient transient Navier–Stokes solver on compact nonuniform space grids

Cited by 23 publications

References 27 publications

Modeling of Shallow-Water Equations by Using Implicit Higher-Order Compact Scheme with Application to Dam-Break Problem

Modeling of Shallow-Water Equations by Using Implicit Higher-Order Compact Scheme with Application to Dam-Break Problem

On a special class of analytical solutions to the three-dimensional incompressible Navier–Stokes equations

Higher-order-compact simulation of unsteady flow past a rotating cylinder at moderate Reynolds numbers

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