Integral conditions for the pressure in the computation of incompressible viscous flows
Journal of Computational Physics
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
An element-by-element BICGSTAB iterative method for three-dimensional steady Navier-Stokes equations
Journal of Computational and Applied Mathematics
Comparison of High-Accuracy Finite-Difference Methods for Linear Wave Propagation
SIAM Journal on Scientific Computing
Multidimensional optimization of finite difference schemes for Computational Aeroacoustics
Journal of Computational Physics
Analysis of anisotropy of numerical wave solutions by high accuracy finite difference methods
Journal of Computational Physics
Hi-index | 31.46 |
In this paper a finite difference scheme is developed within the nine-point semi-discretization framework for the convection-diffusion equation. The employed Pade approximation renders a fourth-order temporal accuracy and the spatial approximation of convection terms accommodates the dispersion relation. The artificial viscosity introduced in the two-dimensional convection-diffusion-reaction (CDR) equation for stability reasons is analytically derived. Constraints on the mesh size and time interval for rendering a monotonic matrix are also rigorously derived. To validate the proposed method, we investigate several problems that are amenable to the exact solutions. The results with good rates of convergence are obtained for the investigated scalar and Navier-Stokes problems.