Adaptive order nodal transport method

High-order nodal transport methods have demonstrated high accuracy and computational efficiency in solving transport problems for systems composed of large homogeneous regions. In addition to these properties, the arbitrarily high order transport method of the nodal type (AHOT-N) possesses simple final equations and allows modifying the order of the spatial approximation without modifying the order of the spatial approximation without modifying the programming of the method. However, AHOT-N requires solving the system with the same order in all nodes and discrete directions. This feature could force the use of more equations and unknowns than needed to obtain a given accuracy with a consequent loss of computational efficiency. In a previous work a slight modification to AHOT-N was presented that allows solving a problem with a different order per node per direction. This was applied in an automatic adaptive order scheme aimed at improving the computational efficiency of AHOT-N and simplifying the error estimation of the obtained solutions. If the problem to be solved does not require a uniform order distribution (UOD), the variable order scheme could reduce significantly the number of equations and unknowns evaluated. In addition, the automatic increasing of the order depending on error estimates avoids the preselection of the order distribution per node per direction necessary to obtain accurate solutions, practically an impossible task that requires extensive knowledge about the shape of the solution. Since the automatic increasing of the method order, depending on the estimated errors, concerns data quality rather than quantity and the optimization of user time rather than CPU time, in this work the authors focus on the behavior of the solutions obtained with the adaptive method