arXiv subjects

Hossein Mahmoodi Darian

Publications and source records attributed to Hossein Mahmoodi Darian.

2 recordsLinked to original sources

arXiv2025

The optimal relaxation parameter for the SOR method applied to the Poisson equation on rectangular grids with different types of boundary conditions

The Successive Over-Relaxation (SOR) method is a useful method for solving the sparse system of linear equations which arises from finite-difference discretization of the Poisson equation. Knowing the optimal value of the relaxation parameter is crucial for fast convergence. In this manuscript, we present the optimal relaxation parameter for the discretized Poisson equation with mixed and different types of boundary conditions on a rectangular grid with unequal mesh sizes in $x$- and $y$-directions ($Δx \neq Δy$) which does not addressed in the literature. The central second-order and high-order compact (HOC) schemes are considered for the discretization and the optimal relaxation parameter is obtained for both the point and line implementation of the SOR method. Furthermore, the obtained optimal parameters are verified by numerical results.

math.NA↗

arXiv2024

Combined WENO schemes for increasing the accuracy of the numerical solution of conservation laws

In this article, we introduce a new method which allows utilizing all the available sub-stencils of a WENO scheme to increase the accuracy of the numerical solution of conservation laws while preserving the non-oscillatory property of the scheme. In this method, near a discontinuity, if there is a smooth sub-stencil with higher-order of accuracy, it is used in the reconstruction procedure. Furthermore, in smooth regions, all the sub-stencils of the same order of accuracy form the stencil with the highest order of accuracy as the conventional WENO scheme. The presented method is assessed using several test cases of the linear wave equation and one- and two-dimensional Euler's equations of gas dynamics. In addition to the original weights of WENO schemes, the WENO-Z approach is used. The results show that the new method increases the accuracy of the results while properly maintaining the ENO property.

physics.comp-ph↗