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Smoothed particle hydrodynamics (SPH) method is a Lagrangian particle method that has been widely used for solving complex mechanics problems. To reduce the SPH computational cost, the adaptive SPH (ASPH) with time-varying particle distribution has been proposed using the particle splitting and merging techniques. However, the particle splitting in the adaptive SPH results in a decreased time step due to the reduced particle spacing and thus requires an increased amount of computing time. In the present work, an explicit Runge-Kutta Chebyshev time stepping scheme is implemented within the adaptive SPH, by including the stabilizing substeps into the Runge-Kutta integration method with the use of the Chebyshev polynomials. The number of stabilizing substeps in a single SPH time step can be adaptive after particle splitting while the Runge-Kutta integration time step remains the same. Therefore, the proposed SPH algorithm is adaptive in both time and space domains. Representative example problems are simulated using the developed time-space adaptive SPH method. It is demonstrated that, as compared to the standard SPH and the conventional adaptive SPH with varying particle distribution only, the presented time-space ASPH method exhibits much higher efficiency without compromising accuracy and the superiority in terms of stability.

Although the environmental and health risks of chlorinated organophosphate esters (OPEs-Cl) have drawn much attention, its environmental behaviors have been insufficiently characterized. As a notable sink of this emerging contaminant, non-sanitary landfills, which may decompose/accumulate OPEs-Cl, is of particular concern. In the present study, the dynamic processes of the typical OPEs-Cl, tris(2-chloroethyl) phosphate (TCEP), in non-sanitary landfill soils were analyzed under anaerobic condition, and the microbial taxa involved in these processes were explored. Our results showed that TCEP could be simultaneously reduced by abiotic and biotic processes, as it was reduced by 73.9% and 65.5% over the 120-day experiment in landfill humus and subsoil, respectively. Notably, the degradation of TCEP was significantly (p 0.05) enhanced under the stress of a high TCEP concentration (10 μg g