Heterogeneous Multiscale Methods: A Review

This paper gives a systematic introduction to HMM,the heterogeneous multiscale methods,including the fundamental design principles behind the HMM philosophy and the main obstacles that have to be overcome when using HMM for a particular problem.This is illustrated by examples from several application areas,including complex fluids,micro-fluidics,solids,interface problems,stochastic problems,and statistically self-similar problems.Emphasis is given to the technical tools,such as the various constrained molecular dynamics,that have been developed,in order to apply HMM to these problems.Examples of mathematical results on the error analysis of HMM are presented.The review ends with a discussion on some of the problems that have to be solved in order to make HMM a more powerful tool.

Numerical simulation of influences of the earth medium's lateral heterogeneity on co- and post-seismic deformation

Many studies revealed that the Earth medium＇s lateral heterogeneity can cause considerable effects on the co- and post-seismic deformation field. In this study, the threedimensional finite element numerical method are adopted to quantify the effects of lateral heterogeneity caused by material parameters and fault dip angle on the co- and postseismic deformation in the near- and far-field. Our results show that： 1） the medium＇s lateral heterogeneity does affect the co-seismic deformation, with the effects increasing with the medium＇s lateral heterogeneity caused by material parameters; 2） the Lame parameters play a more dominant role than density in the effects caused by lateral heterogeneity; 3） when a fault＇s dip angle is smaller than 90, the effects of the medium＇s lateral heterogeneity on the hanging wall are greater than on the footwall; 4） the impact of lateral heterogeneity caused by the viscosity coefficient on the post-seismic deformation can affect a large area, including the near- and far-field.

Slope failure simulations with MPM

The simulation of slope failures,including both failure initiation and development,has been modelled using the material point method（MPM）.Numerical case studies involving various slope angles,heterogeneity and rainfall infiltration are presented.It is demonstrated that,by utilising a constitutive model which encompasses,in a simplified manner,both pre-and post-failure behaviour,the material point method is able to simulate commonly observed failure modes.This is a step towards being able to better quantify slope failure consequence and risk.

Comparison between gradient based UCODE2005 and the ensemble Kalman Filter for transient groundwater flow inverse modeling

Gradient based UCODE_2005 and data assimilation based on the Ensemble Kalman Filter(EnKF) are two different inverse methods. A synthetic two-dimensional flow case with four no-flow boundaries is used to compare the UCODE_2005 with the Ensemble Kalman Filter(EnKF) for their efficiency to inversely calculate and calibrate a hydraulic conductivity field based on hydraulic head data. A zonal, random heterogeneous conductivity field is calibrated by assimilating the time series of heads observed in monitoring wells. The study results indicate that the two inverse methods, UCODE_2005 and EnKF, could be used to calibrate the hydraulic conductivity field to a certain degree. More available observations and information about the conductivity field, more accurate inverse results will be obtained for the UCODE_2005. On the other hand, for a realistic zonal heterogeneous hydraulic conductivity field, EnKF can only efficiently determine the hydraulic conductivity field at the first several assimilated time steps. The results obtained by the UCODE_2005 look better than those by the EnKF. This is possibly due to the fact that the UCODE_2005 uses observed head data at every time step, while EnKF can only use observed heads at first several steps due to the filter divergence problem.