Chebyshev pseudospectral method of viscous flows with corner singularities
Journal of Scientific Computing
Accurate solutions to the square thermally driven cavity at high Rayleigh number
Computers and Fluids
Journal of Computational Physics
A modified Chebyshev pseudospectral method with an O(N–1) time step restriction
Journal of Computational Physics
Essentially compact schemes for unsteady viscous incompressible flows
Journal of Computational Physics
A high order explicit method for the computation of flow about a circular cylinder
Journal of Computational Physics
Comments on a collocation spectral solver for the Helmholtz equation
Journal of Computational Physics
Journal of Computational Physics
Preconditioned multigrid methods for unsteady incompressible flows
Journal of Computational Physics
A Wavelet-Optimized, Very High Order Adaptive Grid and Order Numerical Method
SIAM Journal on Scientific Computing
Galerkin spectral method for the vorticity and stream function equations
Journal of Computational Physics
A penalty method for the vorticity-velocity formulation
Journal of Computational Physics
A compact-difference scheme for the Navier-Stokes equations in vorticity-velocity formulation
Journal of Computational Physics
A vorticity-based method for incompressible unsteady viscous flows
Journal of Computational Physics
A semi-Lagrangian high-order method for Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
Accurate ω-ψ spectral solution of the singular driven cavity problem
Journal of Computational Physics
Numerical investigation on the stability of singular driven cavity flow
Journal of Computational Physics
A new compact spectral scheme for turbulence simulations
Journal of Computational Physics
Journal of Computational Physics
A robust high-order compact method for large eddy simulation
Journal of Computational Physics
Journal of Computational Physics
High order accurate solution of the incompressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
A 2D compact fourth-order projection decomposition method
Journal of Computational Physics
Journal of Computational Physics
A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Grid stabilization of high-order one-sided differencing II: Second-order wave equations
Journal of Computational Physics
Hi-index | 31.46 |
This article presents a family of very high-order non-uniform grid compact finite difference schemes with spatial orders of accuracy ranging from 4th to 20th for the incompressible Navier-Stokes equations. The high-order compact schemes on non-uniform grids developed in Shukla and Zhong [R.K. Shukla, X. Zhong, Derivation of high-order compact finite difference schemes for non-uniform grid using polynomial interpolation, J. Comput. Phys. 204 (2005) 404] for linear model equations are extended to the full Navier-Stokes equations in the vorticity and streamfunction formulation. Two methods for the solution of Helmholtz and Poisson equations using high-order compact schemes on non-uniform grids are developed. The schemes are constructed so that they maintain a high-order of accuracy not only in the interior but also at the boundary. Second-order semi-implicit temporal discretization is achieved through an implicit Backward Differentiation scheme for the linear viscous terms and an explicit Adam-Bashforth scheme for the non-linear convective terms. The boundary values of vorticity are determined using an influence matrix technique. The resulting discretized system with boundary closures of the same high-order as the interior is shown to be stable, when applied to the two-dimensional incompressible Navier-Stokes equations, provided enough grid points are clustered at the boundary. The resolution characteristics of the high-order compact finite difference schemes are illustrated through their application to the one-dimensional linear wave equation and the two-dimensional driven cavity flow. Comparisons with the benchmark solutions for the two-dimensional driven cavity flow, thermal convection in a square box and flow past an impulsively started cylinder show that the high-order compact schemes are stable and produce extremely accurate results on a stretched grid with more points clustered at the boundary.