Compact h4 finite-difference approximations to operators of Navier-Stokes type
Journal of Computational Physics
A perturbational h4 exponential finite difference scheme for the convective diffusion equation
Journal of Computational Physics
High order difference schemes for unsteady one-dimensional diffusion-convection problems
Journal of Computational Physics
Preconditioned iterative methods and finite difference schemes for convection-diffusion
Applied Mathematics and Computation
High order ADI method for solving unsteady convection-diffusion problems
Journal of Computational Physics
High-order compact boundary value method for the solution of unsteady convection-diffusion problems
Mathematics and Computers in Simulation
A high-order exponential scheme for solving 1D unsteady convection-diffusion equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Bi-parameter incremental unknowns ADI iterative methods for elliptic problems
Numerical Algorithms
A new family of (5,5)CC-4OC schemes applicable for unsteady Navier-Stokes equations
Journal of Computational Physics
Hi-index | 7.30 |
n this article, an exponential high-order compact (EHOC) alternating direction implicit (ADI) method, in which the Crank-Nicolson scheme is used for the time discretization and an exponential fourth-order compact difference formula for the steady-state 1D convection-diffusion problem is used for the spatial discretization, is presented for the solution of the unsteady 2D convection--diffusion problems. The method is temporally second-order accurate and spatially fourth order accurate, which requires only a regular five-point 2D stencil similar to that in the standard second-order methods. The resulting EHOC ADI scheme in each ADI solution step corresponds to a strictly diagonally dominant tridiagonal matrix equation which can be inverted by simple tridiagonal Gaussian decomposition and may also be solved by application of the one-dimensional tridiagonal Thomas algorithm with a considerable saving in computing time. The unconditionally stable character of the method was verified by means of the discrete Fourier (or von Neumann) analysis. Numerical examples are given to demonstrate the performance of the method proposed and to compare mostly it with the high order ADI method of Karaa and Zhang and the spatial third-order compact scheme of Note and Tan.