Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations

DOI10.1016/j.amc.2009.10.001zbMath1352.76084OpenAlexW2136898082MaRDI QIDQ846412

Aftab Khan, Li Yuan, Abdullah Shah

Publication date: 9 February 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.10.001

zbMATH Keywords

dual-time steppingincompressible Navier-Stokes equationoscillating plateartificial compressibility methodflux-difference splittingdoubly periodic shear layerKovasznay flow problemTaylor's decaying vorticesupwind compact finite difference

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items (35)

Modified alternating direction-implicit iteration method for linear systems from the incompressible Navier–Stokes equations ⋮ Development of a new type of weighted compact scheme ⋮ Fourth-order central compact scheme for the numerical solution of incompressible Navier–Stokes equations ⋮ Fixing the Residual Flattening of an Upwind Compact Scheme for Steady Incompressible Flows in Enclosed Domains ⋮ A semi-implicit lattice method for simulating flow ⋮ Improvement of weighted compact scheme with multi-step strategy for supersonic compressible flow ⋮ Development of a wavenumber-preserving scheme for solving Maxwell's equations in curvilinear non-staggered grids ⋮ Numerical solution of a phase field model for incompressible two-phase flows based on artificial compressibility ⋮ On modified block SSOR iteration methods for linear systems from steady incompressible viscous flow problems ⋮ On approximated ILU and UGS preconditioning methods for linearized discretized steady incompressible Navier-Stokes equations ⋮ The estimation of truncation error by \(\tau\)-estimation for Chebyshev spectral collocation method ⋮ Structural schemes for one dimension stationary equations ⋮ Solving singular boundary value problems using higher-order compact finite difference schemes with a novel higher-order implementation of Robin boundary conditions ⋮ Approximate deconvolution discretisation ⋮ Performance of compact and non-compact structure preserving algorithms to traveling wave solutions modeled by the Kawahara equation ⋮ A continuously differentiable upwinding scheme for the simulation of fluid flow problems ⋮ High-order upwind compact finite-difference lattice Boltzmann method for viscous incompressible flows ⋮ On preconditioned iterative methods for unsteady incompressible Navier-Stokes equations ⋮ Coupled problem of the inverse design and constraint optimization ⋮ On the comparison between compact finite difference and pseudospectral approaches for solving similarity boundary layer problems ⋮ A new fourth‐order numerical algorithm for a class of three‐dimensional nonlinear evolution equations ⋮ A new approximate analytical solutions for two- and three-dimensional unsteady viscous incompressible flows by using the kinetically reduced local Navier-Stokes equations ⋮ Compact finite difference relaxation method for chaotic and hyperchaotic initial value systems ⋮ Higher order compact finite difference schemes for unsteady boundary layer flow problems ⋮ A new fourth-order numerical algorithm for a class of nonlinear wave equations ⋮ Numerical Simulation of the Coupled Sine-Gordon Equations via a Linearized and Decoupled Compact ADI Method ⋮ A new high accuracy two-level implicit off-step discretization for the system of two space dimensional quasi-linear parabolic partial differential equations ⋮ Application of compact finite-difference schemes to simulations of stably stratified fluid flows ⋮ A preconditioned lattice Boltzmann flux solver for steady flows on unstructured hexahedral grids ⋮ Unnamed Item ⋮ Sixth-order compact finite difference scheme with discrete sine transform for solving Poisson equations with Dirichlet boundary conditions ⋮ Second-order entropy satisfying BGK-FVS schemes for incompressible Navier-Stokes equations ⋮ The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations ⋮ High-order compact difference schemes on wide computational stencils with a spectral-like accuracy ⋮ A less time-consuming upwind compact difference method with adjusted dissipation property for solving the unsteady incompressible Navier-Stokes equations

Uses Software

• Fluid flow phenomena

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compact high-order accurate nonlinear schemes
• High-order accurate solution of the incompressible Navier--Stokes equations
• Analysis of a new high resolution upwind compact scheme
• Very high-order compact finite difference schemes on non-uniform grids for incompressible Navier-Stokes equations
• Application of a fractional-step method to incompressible Navier-Stokes equations
• A diagonal form of an implicit approximate-factorization algorithm
• Approximate Riemann solvers, parameter vectors, and difference schemes
• An upwind differencing scheme for the incompressible Navier-Stokes equations
• Compact finite difference schemes with spectral-like resolution
• Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique
• Polynomial interpolation methods for viscous flow calculations
• Implicit weighted ENO schemes for the three-dimensional incompressible Navier-Stokes equations
• On performance of methods with third- and fifth-order compact upwind differencing
• A high order accurate difference scheme for complex flow fields
• Performance of under-resolved two-dimensional incompressible flow simulations. II
• Factorization methods for the numerical approximation of Navier-Stokes equations
• Conservative hybrid compact-WENO schemes for shock-turbulence interaction
• Comparison of implicit multigrid schemes for three-dimensional incompressible flows
• Implicit lower-upper/approximate-factorization schemes for incompressible flows
• A second-order projection method for the incompressible Navier-Stokes equations
• Essentially compact schemes for unsteady viscous incompressible flows
• A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems
• A compact difference scheme for the Navier-Stokes equations in vorticity-velocity formulation
• Spectral/\(hp\) penalty least-squares finite element formulation for the steady incompressible Navier-Stokes equations
• High-resolution finite compact difference schemes for hyperbolic conservation laws
• A numerical method for solving incompressible viscous flow problems
• A calculation procedure for heat, mass and momentum transfer in three- dimensional parabolic flows
• Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
• Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations
• Application of time-iterative schemes to incompressible flow
• A Fortran subroutine for the solution of periodic block-tridiagonal systems
• An Implicit Factored Scheme for the Compressible Navier-Stokes Equations
• High-order accurate numerical solutions of incompressible flows with the artificial compressibility method
• A compact fourth‐order finite difference scheme for the steady incompressible Navier‐Stokes equations
• Practical aspects of higher-order numerical schemes for wave propagation phenomena
• Numerical Solution of the Navier-Stokes Equations
• Moving Mesh Finite Element Methods for the Incompressible Navier--Stokes Equations
• Fluid flow phenomena. A numerical toolkit. Incl. 1 disk

This page was built for publication: Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations