Evaluation of Numerical Simulation Methods for Shock Waves Using Analytical Hierarchy Process and Fuzzy Analytical Hierarchy Process

Dam break in recent decades has caused extensive damage to infrastructure and economic activities.Recently, the finite volume method based on shallow water equations with the ability to model shock waves has been welcomed by many researchers due to the high resolution of this method in the modeling of various supercritical, subcritical, steady, unsteady, continuous and discontinuous flows.. The five widely used methods are HLL, HLLC, Osher, FVS and REF (Roe with Entropy Fixed). Important features of mentioned numerical methods include five factors of accuracy, simulation time, ease of implementation, applicability for different issues and stability. The Analytical Hierarchy Process (AHP) and  Fuzzy Analytical Hierarchy Process (FAHP) provide convenient approaches for solving complex Multi-Criteria Decision-Making (MCDM) problems in engineering.Each methods are evaluated in terms of the decision criteria based on the weight of each criterion and pairwise comparisons are used to determine the relative importance of each method in terms of each criterion. Pairwise comparisons are quantified by using a scale.The results show that the Osher method appear to be superior to the other types of approximate Riemann solvers. Then the HLLC and the FVS methods, with slight difference in weight, are ranked next.