ارزيابي روش‌هاي شبيه‌سازي عددي امواج شوك با استفاده از فرايند تحليل سلسله مراتبي فازي و غيرفازي

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

مسئله شكست سد كه در اثر رها شدن ناگهاني حجمي از آب در يك آبراهه اتفاق مي‌افتد، شامل امواج شوك و انبساطي مي‌شود. از آنجا كه اين پديده باعث ايجاد خسارات مالي و جاني مي‌شود، حائز اهميت است. با توجه به اهميت مسئله شكست سد تاكنون روش هاي مختلفي براي مدلسازي عددي امواج ناشي از آن ارائه شده است. در سال‌هاي اخير روش حجم محدود مبتني بر معادلات آب كم عمق با توانايي مدلسازي امواج شوك، به عنوان روشي پيشرو مورد استقبال محققين زيادي قرار گرفته است كه دليل اين امر توانايي بالاي اين روش در مدلسازي انواع جريان‌هاي فوق بحراني، زير بحراني، دائمي، غير دائمي، پيوسته و ناپيوسته است. در تحقيق حاضر عملكرد پنج روش از روش‌هاي پركاربرد ارائه شده توسط محققين كه مهمترين حل كننده‌هاي تقريبي مسئله ريمان به شمار مي‌روند با توجه به معيارهاي دقت، زمان شبيه‌سازي، سهولت اجرا، قابليت كاربرد و پايداري مورد بررسي قرار گرفته و سپس با استفاده از فرايند تحليل سلسله مراتبي (AHP) و فرايند تحليل سلسله مراتبي فازي (FAHP) روش بهينه معرفي شده است. نتايج هر دو روشAHP و FAHP نشان دهنده برتري روش Osher نسبت به ساير روش هاست.سپس روش‌هاي HLLC و FVS با اختلاف كمي در رتبه بعد قرار مي‌گيرند.

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.