A compact finite differences exact projection method for the Navier–Stokes equations on a staggered grid with fourth-order spatial precision

Reis, Gabriela Aparecida dos; Tasso, Italo Valença Mariotti; Souza, Leandro Franco de; Cuminato, José Alberto

doi:10.1016/j.compfluid.2015.06.015

Cited by 19 publications

(14 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For the Dirichlet-type boundary condition, the one-sided fourth-order compact scheme proposed by [51] is used, which is…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…The applications of their method were given in [43]. In recent years, there has been increasing interest in utilizing the compact difference scheme for spatial discretization of the incompressible Navier-Stokes equations combined with the projection method for velocity-pressure decoupling [44][45][46][47][48][49][50][51][52][53]. Differences among these works can be classified into three aspects: (a) the first is the grid arrangement.…”

Section: Introductionmentioning

confidence: 99%

“…Boersma [49] and Tyliszczak [50] both solved the Poisson equation iteratively using the GMRESR algorithm. Reis et al [51] reformulated the Poisson equation into a set of first-order differential equations, thus more efficient direct or iterative solvers for the sparse system could be used, but the computational cost was increased. On a half-staggered grid, Laizet and Lamballais [48] transformed and solved the Poisson equation in spectral space by the fast Fourier transform (FFT), and then obtained the solution in physical space by the inverse Fourier transform efficiently.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows

Wang

et al. 2018

Computation

View full text Add to dashboard Cite

In the present work, a highly efficient incompressible flow solver with a semi-implicit time advancement on a fully staggered grid using a high-order compact difference scheme is developed firstly in the framework of approximate factorization. The fourth-order compact difference scheme is adopted for approximations of derivatives and interpolations in the incompressible Navier-Stokes equations. The pressure Poisson equation is efficiently solved by the fast Fourier transform (FFT). The framework of approximate factorization significantly simplifies the implementation of the semi-implicit time advancing with a high-order compact scheme. Benchmark tests demonstrate the high accuracy of the proposed numerical method. Secondly, by applying the proposed numerical method, we compute turbulent channel flows at low and moderate Reynolds numbers by direct numerical simulation (DNS) and large eddy simulation (LES). It is found that the predictions of turbulence statistics and especially energy spectra can be obviously improved by adopting the high-order scheme rather than the traditional second-order central difference scheme.

show abstract

“…For the Dirichlet-type boundary condition, the one-sided fourth-order compact scheme proposed by [51] is used, which is…”

Section: Spatial Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows

Wang

et al. 2018

Computation

View full text Add to dashboard Cite

show abstract

“…O esquema LP-E possui a interessante característica de produzir segunda ordem de convergência, sem a necessidade de se incluir uma aproximação para o gradiente da pressão na equação do momento e sem a necessidade de corrigir as condições de contorno para u * . Visto que não foi encontrado na literatura método de projeção com as características do LP-E, esse método foi publicado no Journal Computer & Fluids [39]. Os próximos resultados utilizam apenas o LP-E.…”

Section: Resultsunclassified

“…• Desenvolvimento de um método de projeção para as equações de Navier-Stokes com variáveis primitivas e em malha deslocada [39,40]. Esse método é totalmente baseado em diferenças finitas compactas, incluindo a equação de Poisson.…”

Section: Introductionunclassified

Estudo de métodos de interface imersa para as equações de Navier-Stokes

Reis¹

View full text Add to dashboard Cite

A great limitation of finite differences methods is that they are restricted to retangular meshes and domains. In order to describe flows in complex domains, e.g. free surface problems, it is necessary to use accessory techniques. The immersed interface method is one of such techniques. In the present work, firstly, a projection method was developed, which is completely pressure-free, for the Navier-Stokes equations with primitive variables in a staggered mesh. This method is based on compact finite differences, with temporal second-order precision and spatial foruth-order precision. This method was combined with the immersed interface method from Linnick e Fasel [2] in order to numerically solve the Stokes equations with fourth-order precision. The verification of the code was performed with the manufactured solutions method and by comparing results with other authors for some classical problems in the literature.

show abstract

Simulation of the incompressible Navier–Stokes via integrated radial basis function based on finite difference scheme

Ebrahimijahan

Dehghan

Abbaszadeh

2022

Engineering with Computers

View full text Add to dashboard Cite

A compact finite differences exact projection method for the Navier–Stokes equations on a staggered grid with fourth-order spatial precision

Cited by 19 publications

References 49 publications

Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows

Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows

Estudo de métodos de interface imersa para as equações de Navier-Stokes

Simulation of the incompressible Navier–Stokes via integrated radial basis function based on finite difference scheme

Contact Info

Product

Resources

About