Wave propagation in generalized thermo-poro-elastic media via wavelet-based cell-adaptive central high resolution schemes using UNO limiters

Abstract

The uniformly non-oscillatory (UNO) limiters with second-order accuracy are updated to handle nonuniform cell obtained from wavelet-based cell adaptation. These limiters are then used in the cell-adaptive second-order Kurganov-Tadmor (KT) central high resolution scheme. Over the adapted cells, the performance of the UNO limiters are compared with the generalized MINMOD (GMM) limiter with the total variation diminishing (TVD) feature, by measuring error of reconstruction of some functions and also by numerical solution of some benchmark partial differential equations (PDEs). Then, unified forms of generalized fully-coupled saturated thermo-poro-elastic systems are presented as first-order hyperbolic-parabolic systems in the 2D Cartesian and the asymmetric spherical coordinates. For these systems, corresponding flux, source (load), diffusion and nonlinear terms are derived. It is shown that in the case of the asymmetric spherical coordinate, due to the geometry, considerable complexities are introduced in the load (source) and flux terms. Finally, the coupled 1D and 2D systems are simulated by the adaptive central KT scheme with the GMM and UNO limiters.