Simulation of generalized saturated thermo-elastic media in axisymmetric cylindrical coordinate by cell-adaptive central high-resolution schemes with compression-adaptive UNO slope limiters

Purpose The purpose of this study is to (1) improve the spectral features of the second-order uniformly non-oscillatory (UNO) slope limiters, and (2) numerical simulation of the unified-form of generalized fully-coupled saturated thermo-poro-elastic systems in the axisymmetric cylindrical coordinate via cell-adaptive Kurganov-Tadmor (KT) central high-resolution scheme using the UNO limiters. Design/methodology/approach (1) The spectral features of the UNO limiter are improved by compression-adaptive MINMOD (MM) limiters, achieved by blending different types of MM limiters to achieve less numerical dissipation and dispersion. These blended MM limiters preserve the total variation diminishing (TVD) feature over non-uniform non-centered cells. Also, the spectral features of the central schemes using the UNO limiters are investigated. (2) For the thermo-poro-elastic problem, corresponding first-order hyperbolic system is provided, including flux, source, diffusion and nonlinear terms. Where, there are different interacting components in the source and flux terms. The nonlinear terms are also considered by the Picard-like linearization concept. Findings Compression-adaptive UNO limiters would be stable over adapted cells with centered and non-centered cells. The benchmarks confirm that both spectral features and numerical accuracy are improved. For the generalized thermo-poro-elastic problem, corresponding responses including the shock waves can properly be captured. Originality/value Studying heat effects (e.g. hot fluid or freezing) and explosions on tunnels. Also, the UNO limiters could be used for simulations of various systems of conservation laws.