Lattice Boltzmann method for the fractional advection-diffusion equation

Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β , the fractional order α , and the single relaxation time τ , the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering

Landslide susceptibility mapping using support vector machine and GIS at the Golestan province, Iran

The main goal of this study is to produce landslide susceptibility map using GIS-based support vector machine (SVM) at Kalaleh Township area of the Golestan province, Iran. In this paper, six different types of kernel classifiers such as linear, polynomial degree of 2, polynomial degree of 3, polynomial degree of 4, radial basis function (RBF) and sigmoid were used for landslide susceptibility mapping. At the first stage of the study, landslide locations were identified by aerial photographs and field surveys, and a total of 82 landslide locations were extracted from various sources. Of this, 75% of the landslides (61 landslide locations) are used as training dataset and the rest was used as (21 landslide locations) the validation dataset. Fourteen input data layers were employed as landslide conditioning factors in the landslide susceptibility modelling. These factors are slope degree, slope aspect, altitude, plan curvature, profile curvature, tangential curvature, surface area ratio (SAR), lithology, land use, distance from faults, distance from rivers, distance from roads, topographic wetness index (TWI) and stream power index (SPI). Using these conditioning factors, landslide susceptibility indices were calculated using support vector machine by employing six types of kernel function classifiers. Subsequently, the results were plotted in ArcGIS and six landslide susceptibility maps were produced. Then, using the success rate and the prediction rate methods, the validation process was performed by comparing the existing landslide data with the six landslide susceptibility maps. The validation results showed that success rates for six types of kernel models varied from 79% to 87%. Similarly, results of prediction rates showed that RBF (85%) and polynomial degree of 3 (83%) models performed slightly better than other types of kernel (polynomial degree of 2 = 78%, sigmoid = 78%, polynomial degree of 4 = 78%, and linear = 77%) models. Based on our results, the differences in the rates (success and prediction) of the six models are not really significant. So, the produced susceptibility maps will be useful for general land-use planning