Compact h4 finite-difference approximations to operators of Navier-Stokes type
Journal of Computational Physics
High accuracy solutions of incompressible Navier-Stokes equations
Journal of Computational Physics
High order difference schemes for unsteady one-dimensional diffusion-convection problems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
High order ADI method for solving unsteady convection-diffusion problems
Journal of Computational Physics
Dimension splitting for evolution equations
Numerische Mathematik
A numerical scheme for particle-laden thin film flow in two dimensions
Journal of Computational Physics
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A high-order compact alternating direction implicit (ADI) method is proposed for solving two-dimensional (2D) parabolic problems with variable coefficients. The computational problem is reduced to sequence one-dimensional problems which makes the computation cost-effective. The method is easily extendable to multi-dimensional problems. Various numerical tests are performed to test its high-order accuracy and efficiency, and to compare it with the standard second-order Peaceman-Rachford ADI method. The method has been applied to obtain the numerical solutions of the lid-driven cavity flow problem governed by the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation. The solutions obtained agree well with other results in the literature.