پديد آورندگان :
ضياالديني دشتخاكي، مريم دانشگاه شهيد باهنر كرمان - دانشكده فني و مهندسي - بخش مهندسي عمران , حسامي كرماني، مسعود رضا دانشگاه شهيد باهنر كرمان - دانشكده فني و مهندسي - بخش مهندسي عمران , قائيني حصاروئيه، مهناز دانشگاه شهيد باهنر كرمان - دانشكده فني و مهندسي - بخش مهندسي عمران
كليدواژه :
تحليل سلسله مراتبي , تحليل سلسله مراتبي فازي , امواج شوك , حل كننده‌هاي تقريبي ريمان , بهينه سازي
چكيده لاتين :
Dam break in recent decades has caused extensive damage to infrastructure and economic activities in
different parts of the world, so the study of this phenomenon is considered as one of the most important
issues in hydraulic engineering. Considering the importance of the dam break, various methods have
been proposed for numerical modeling of the resulting waves. 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 shallow water equations are nonlinear and
their solution is limited to a certain number of states, such as the approximate Riemann solvers. Several
types of approximate Riemann solvers have been suggested that are more economical than the exact
solution of the Riemann problem. The five widely used methods are HLL (Harten-Lax-van Leer), HLLC
(Harten-Lax-van Leer-Contact) designed as an improvement to the classical HLL, Osher, FVS (Flux
Vector Splitting) 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. The AHP and the FAHP are the decision support tools which can be
used to solve complex decision problems. They use a multi-level hierarchical structure of objectives,
criteria, subcriteria, and alternatives. In the present study, the performance of the five widely used
methods by researchers, which are the most important approximation solvers of the Riemann problem,
are investigated according to the criteria of accuracy, simulation time, ease of implementation,
applicability and stability based on AHP and FAHP. 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. In the AHP and the FAHP the pairwise comparisons in a judgment matrix are considered to be
adequately consistent, as the corresponding consistency ratio was less than 10%. The AHP and the FAHP
yielded the same ranking for the five methods. The final computed weights based on the AHP for Osher,
HLLC, FVS, HLL and REF methods are 0.285, 0.198, 0.199, 0.161 and 0.156 respectively. The FAHP
final computed weights for Osher, HLLC, FVS, HLL and REF methods are 0.282, 0.200, 0.198, 0.164
and 0.156 respectively. The results of both the AHP and the FAHP methods 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, and finally the HLL and the REF methods are
in the fourth and fifth priorities. The FVS method, despite being the fastest method for modeling, did not
rank first due to the ability of the AHP and the FAHP methods, which take into account different criteria.
