مقايسه مدل‌هاي محلي آشوبناك مبتني بر فضاي فاز در پيش‌بيني جريان رودخانه

Comparison between phase space-based local chaotic models for riverflow forecasting

روش هاي بدون شبكه (لاگرانژي)، مانند روش نيمه ضمني ذرات متحرك (MPS) و هيدروديناميك ذرات هموار (SPH)، جديدترين نسل از اين روش ها در زمينه ديناميك سيالات محاسباتي است كه توجه پژوهشگران را در مسايل كاربردي، كه در آن‌ها تغييرشكل‌هاي بزرگ و ناپيوستگي جريان وجود دارد، به خود جلب كرده اند. هدف از اين پژوهش، توسعه و بهبود شبيه‌سازي جريان‌هاي با سطح آزاد با استفاده از مدل جديد نيمه ضمني ذرات متحرك با تراكم پذيري ضعيف (WC-MPS) است. به شكل معمول، در روشMPS ، تعيين فشار سيال با حل ضمني معادله پواسون صورت مي‌گيرد كه مستلزم صرف زمان زياد براي رايانه است. در روش نيمه ضمني ذرات متحرك با تراكم پذيري ضعيف، مشابه روش SPH، از معادله حالت كه به صورت صريح حل شده و وقت زيادي از رايانه اشغال نمي نمايد، بهره گرفته شده است. به منظور ارزيابي روش و مدل پيشنهادي، مسيله شناخته شده و پركاربرد جريان ناشي از شكست يك سد مورد بررسي قرار گرفته است. برنامه نويسي به زبان C انجام گرفته و آزمايش هاي درستي آزمايي در خصوص كد نوشته شده صورت گرفت. براي مقايسه رويكرد لاگرانژي با رويكرد اويلري، شكست سد به وسيله‌ي نرم افزار FLOW-3D نيز مدل سازي شده است. نتايج بررسي ها و مقايسه با نتايج آزمايشگاهي نشان مي دهد كه هر دو رويكرد داراي دقت قابل قبولي در مدل سازي جريان با سطح آزاد است. ليكن، دقت رويكرد لاگرانژي، به ويژه روش WC-MPS ارايه شده، نسبت به رويكرد اويلري بيشتر است. روش پيشنهادي داراي نوسانات فشار بوده و در ادامه راهكارهاي كاهش اين نوسانات بررسي شده است.

Mesh-free (Lagrangian) methods, such as moving particle semi-implicit (MPS) and smoothed particle hydrodynamics (SPH) methods belong to the latest generation of computationaal fluid dynamics, which have attacted attention of researchers in applied problems where there are large deformations and fragmentations. This study aims to develop and characterize a MPS (based on a weakly compressible formulation, WC-MPS) model for prediction of flow characteristics. Usually, in MPS method, fluid pressure is determined implicitly by solving Poisson equation, which requires a lot of computer time. In WC-MPS method, similar to SPH method, explicitly-solved state equation is used, which doesnʹt need too much computer time. The governing equations for fluid flow, including mass conservation and movement distance, are transformed to interaction equations between the particles, by using different operators. In this respect, the nearer particles to the specified particle have more impact on the particle and the effect of distant particles is neglected. The interaction of particles is weighed by a function, called kernel function. To solve the governing equation in MPS method, the equations are written at two time levels of present and future. Discretization of Navier-Stokeʹs equation was performed at two semi-step time scale. Turbulence equation was Gotohʹs equation. Boundary conditions are applied such that in addition to simplification, the physical conditions of the phenomenon, including particle density at boundaries, are not much different from the rest of the flow domain. To assess the proposed method and model, the well-known and applied problem of fluid flow due to dam break was investigated. Programming was in C language and validation tests were performed for the written computer code. To compare Lagrangian and Eulerian approaches, dam break was modeled with Flow-3D software, too. Results of the modeling and comparison with experimental data showed that both approaches gave acceptable results in modeling of free-surface flows. But, the Lagrangian approach, especially the WC-MPS method, was more accurate than Eulerian approach. Lagrangian-based methods had especial ability in prediction of free-surface profile, even when there were great deformations in the water surface. The proposed method had pressure turbulences, which was investigated for their reduction. MPS method, due to solving the pressure equation explicitly, is more precise than SPH method. But, computational time is greater in this method. Weak-compressibility hypothesis in MPS method reduces artificial pressure turbulences. In modeling the positive and negative wave fronts in dam break problem, it was revealed that Lagrangian approach was more accurate than Eulerian approach. Comparison of WC-MPS and IISPH methods in Lagrangian approach showed that both methods have similar accuracy, but less number of particles was used in simulation process in WC-MPS method.