Application Of Spectral Element Method Research Articles

Application of spectral element method in simulation of fractured porous media domains modeled by fracture-only technique

In this paper, a new application of the spectral element method (SEM) is proposed, which is combined by the features of the fracture-only reservoir simulation technique. This method has been examined with the numerical simulation of waterflooding recovery mechanism. The effect of co-current imbibition is exhibited by a fracture flow analysis with an impermeable porous media. This analysis has been then repeated to study counter-current imbibition effect considering a homogeneous porous media. The capability of the fracture-only technique has been demonstrated more by analyzing fracture flow with heterogeneous porous media. All the presented SEM's results have shown a closeness agreement with the valid results obtained by analytical and streamline-based formulations. The SEM presented 36% higher accuracy when compared to the solution obtained by the finite element method (FEM).

Application of spectral element method for solving Sobolev equations with error estimation

This paper is dedicated to numerically solving the Sobolev equations that have several applications in physics and mechanical engineering. First, the temporal derivative is discretized by the Crank-Nicolson finite difference technique to obtain a semi-discrete scheme in the temporal direction. Afterward, the stability and convergence analysis of the time semi-discrete scheme are proven by applying the energy method. It also implies that the convergence order in the temporal direction is O(dt2). Second, a fully discrete formula has been acquired by discretizing the spatial derivatives via Legendre spectral element method (LSEM). This method applies the Lagrange polynomial based on the Gauss-Legendre-Lobatto (GLL) points. Moreover, an error estimation is given for the obtained fully discrete scheme. Eventually, the two-dimensional Sobolev equations are solved by using the proposed procedure. The accuracy and efficiency of the mentioned procedure are demonstrated by several numerical examples.

Application of Spectral Element Method Combining Dilatation Theory to Sound Generated by a Co-rotating Vortex Pair

Application of Spectral Element Method Combining Dilatation Theory to Sound Generated by a Co-rotating Vortex Pair