Book ChapterDOI
A Fourth-Order Iterative Solver for the Singular Poisson Equation
Stéphane Abide,Xavier Chesneau,Belkacem Zeghmati +2 more
- pp 143-150
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TLDR
A compact fourth-order finite difference scheme solver devoted to the singular-Poisson equation is proposed and verified andumerical results show that the new proposed Poisson solver is efficient while retaining the fourth- order compact accuracy.Abstract:
A compact fourth-order finite difference scheme solver devoted to the singular-Poisson equation is proposed and verified The solver is based on a mixed formulation: the Poisson equation is splitted into a system of partial differential equations of the first order This system is then discretized using a fourth-order compact scheme This leads to a sparse linear system but introduces new variables related to the gradient of an unknow function The Schur factorization allows us to work on a linear sub-problem for which a conjugated-gradient preconditioned by an algebraic multigrid method is proposedNumerical results show that the new proposed Poisson solver is efficient while retaining the fourth-order compact accuracyread more
Citations
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Journal ArticleDOI
An efficient parallel high-order compact scheme for the 3D incompressible Navier–Stokes equations
TL;DR: A new strategy for solving the Helmholtz/Poisson equations based on a parallel 2d-pencil decomposition of the diagonalisation method, which achieves good parallel performances by introducing a bounded numerical error.
Journal ArticleDOI
Higher-order compact scheme for high-performance computing of stratified rotating flows
TL;DR: A scalable numerical method, based on higher-order compact scheme, is described to solve rotating stratified flows in cylindrical annular domains and is found to drastically reduce the huge execution times often preventing detailed numerical investigations of these complex phenomena.
References
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Book
Computational methods for fluid dynamics
Joel H. Ferziger,Milovan Perić +1 more
TL;DR: This text develops and applies the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice, including advanced techniques in computational fluid dynamics.
Journal ArticleDOI
Compact finite difference schemes with spectral-like resolution
TL;DR: In this article, the authors present finite-difference schemes for the evaluation of first-order, second-order and higher-order derivatives yield improved representation of a range of scales and may be used on nonuniform meshes.
Journal Article
An aggregation-based algebraic multigrid method
TL;DR: Numerical results indicate that the proposed algebraic multigrid method may be significantly more robust as black box solver than the classical AMG method as implemented in the code AMG1R5 by K. Stuben.
Journal ArticleDOI
A robust high-order compact method for large eddy simulation
TL;DR: In this paper, a high-order compact method for large eddy simulation (LES) of compressible turbulent flows is presented, which is applicable to the conservative form of the governing equations, thereby allowing total energy conservation.