An analysis of 1-D smoothed particle hydrodynamic kernels

The key element in smoothed particle hydrodynamics (SPH), the SPH kernel, is analyzed with two objectives: to develop a measure of merit for evaluating kernels in one-dimensional SPH and to apply this measure to 20 different kernels, providing an insight into the use of these kernels in SPH. In particular, through a static validation test and the theory developed here, it is concluded that the key variables in a kernel's worth are the shape and the value of Delta x/h. This measure of merit provides an objective method based on problem information of determining a set of kernels that should provide better results. Based on an analysis of 20 kernels, it is shown that bell-shaped kernels tend to outperform other shapes for SPH regions of smooth data. (AIAA)