A high order finite-difference scheme for time-domain modelling of time-varying seismoelectric waves

Simulation of the seismoelectric effect serves as a useful tool to capture the observed seismoelectric conversion phenomenon in porous media, thus offering promising potential in underground exploration activities to detect pore fluids such as water, oil and gas. The static electromagnetic (EM) approximation is among the most widely used methods for numerical simulation of the seismoelectric responses. However, the static approximation ignores the accompanying electric field generated by the shear wave, resulting in considerable errors when compared to analytical results, particularly under high salinity conditions. To mitigate this problem, we propose a spatial high-order finite-difference time-domain (FDTD) method based on Maxwell's full equations of time-varying EM fields to simulate the seismoelectric response in 2D mode. To improve the computational efficiency influenced by the velocity differences between seismic and electromagnetic waves, different time steps are set according to the stability conditions, and the seismic feedback values of EM time nodes are obtained by linear approximation within the seismic unit time step. To improve the simulation accuracy of the seismoelectric response with the time-varying EM calculation method, finite-difference coefficients are obtained by solving the spatial high-order difference approximation based on Taylor expansion. The proposed method yields consistent simulation results compared to those obtained from the analytical method under different salinity conditions, thus indicating its validity for simulating seismoelectric responses in porous media. We further apply our method to both layered and anomalous body models and extend our algorithm to 3D. Results show that the time-varying EM calculation method could effectively capture the reflection and transmission phenomena of the seismic and EM wavefields at the interfaces of contrasting media. This may allow for the identification of abnormal locations, thus highlighting the capability of seismoelectric response simulation to detect subsurface properties.

Fully Coupled Numerical Methods for Elastohydrodynamic Lubrication Line Contact Problems by the High Order Finite Difference Methods

In this paper a high order finite difference method is constructed to solve the elastohydrodynamic lubrication line contact problems, whose cavitation condition is handled by the penalty method. The highly nonlinear equations from the discretization of the high order finite difference method are solved by the trust-region dogleg algorithm. In order to reduce the numerical dissipation and dispersion brought by the high order upwind finite difference scheme, a high order biased upwind finite difference scheme is also presented. Our method is found to achieve more accurate solutions using just a small number of nodes compared to the multilevel methods combined with the lower order finite difference method.

Direct steady-state solutions for circuit models of nonlinear electromagnetic devices

Purpose This paper aims to omit the difficulties of directly finding the periodic steady-state solutions for electromagnetic devices described by circuit models. Design/methodology/approach Determine the discrete integral operator of periodic functions and develop an iterative algorithm determining steady-state solutions by a multiplication of matrices only. Findings An alternative method to creating finite-difference relations directly determining steady-state solutions in the time domain. Research limitations/implications Reduction of software and hardware requirements for determining steady-states of electromagnetic. Practical implications A unified approach for directly finding steady-state solutions for ordinary nonlinear differential equations presented in the normal form. Originality/value Eliminate the necessity of solving high-order finite-difference equations for steady-state analysis of electromagnetic devices described by circuit models.