A high-order SPH method by introducing inverse kernels

The smoothed particle hydrodynamics (SPH) method is usually expected to be an effi-cient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the problem of low-order consistency. A high-order SPH method by intro-ducing inverse kernels, which is quite easy to be implemented but efficient, is proposed for solving this restriction. The basic inverse method and the special treatment near boundary are introduced with also the discussion of the combination of the Least-Square (LS) and Moving-Least-Square (MLS) methods. Then detailed analysis in spectral space is presented for people to better under-stand this method. Finally we show three test examples to verify the method behavior.     

Detection of Envisat RA2/ICE-1 retracked radar altimetry bias over the Amazon basin rivers using GPS

Altimetry is now routinely used to monitor stage variations over rivers, including in the Amazon basin. It is desirable for hydrologic studies to be able to combine altimetry from different satellite missions with other hydrogeodesy datasets such as leveled gauges and watershed topography. One requirement is to accurately determine altimetry bias, which could be different for river studies from the altimetry calibrated for deep ocean or lake applications. In this study, we estimate the bias in the Envisat ranges derived from the ICE-1 waveform retracking, which are nowadays widely used in hydrologic applications. As a reference, we use an extensive dataset of altitudes of gauge zeros measured by GPS collocated at the gauges. The thirty-nine gauges are spread along the major tributaries of the Amazon basin. The methodology consists in jointly modeling the vertical bias and spatial and temporal slope variations between altimetry series located upstream and downstream of each gauge. The resulting bias of the Envisat ICE-1 retracked altimetry over rivers is 1.044 ± 0.212 m, revealing a significant departure from other Envisat calibrations or from the Jason-2 ICE-1 calibration.