اصلاح شرايط مرزي روش هيدروديناميك ذرات هموار در مدل سازي بالاروي موج با استفاده از قابليت پردازش موازي

Improving Boundary Condition in Wave Run-up Simulation using SPH-GPU

بالاروي موج يكي از عوامل مهم در طراحي سازه­هاي ساحلي است و تخمين مناسب آن در تعيين تراز طراحي سازه­هاي دريايي تاثير دارد. بالاروي و شكست موج، باعث تغييرات و بهم ريختگي زياد سطح آب مي‌شود كه با توجه به قابليت روش هيدروديناميك ذرات هموار در شبيه سازي اين پديده، از اين روش در پژوهش حاضر استفاده شده است. يكي از عوامل تأثيرگذار بر بالاروي، تنش بستر است كه اعمال آن مي‌تواند باعث بهبود نتايج گردد. در اين راستا، در اين پژوهش با معرفي دو رويكرد جديد، مدل عددي SPH بگونه‌اي توسعه يافت كه نيروي اصطكاك با دو رويكرد متفاوت به ذرات مجاور مرز اعمال گردد. نتايج اين مدل با روابط تحليلي-تجربي معتبر مقايسه و مشاهده گرديد كه با تصحيح مدل، دقت افزايش يافته و ميزان بالاروي با مقدار خطاي كم‌تري ارزيابي مي‌گردد. بر اساس نتايج به‌دست آمده، اعمال نيروي اصطكاك تأثير بسزايي بر پاسخ‌ها دارد و ميزان بهبود نتايج وابسته به هندسه و شرايط موج است. اگر بالاروي همراه با لغزش موج روي سطح بستر باشد، تاثير اعمال نيروي اصطكاك بر بهبود نتايج افزايش مي‌يابد به‌نحوي‌كه در بعضي از مدل­ها خطاي 90 درصدي را به 6 درصد كاهش مي­دهد. با توجه به هزينه محاسباتي بالاي روش SPH نسبت به ساير روش‌هاي مرسوم عددي، از قابليت پردازش موازي و استفاده از ظرفيت كارت گرافيك به‌منظور كاهش زمان محاسبات استفاده شد. همچنين، براي ارزيابي عملكرد اين مدل، هزينه محاسباتي گام‌هاي مختلف روش توسعه يافته در هر دو شرايط استفاده و عدم استفاده از پردازش موازي با يكديگر مقايسه گرديد.

Wave run up elevations and wave overtopping rate are two important parameters in design of coastal structures specially in definition of their crest elevation. Wave run up in contribution with wave breaking generates local turbulences as well as large deformations around free surface profile. Smoothed Particle Hydrodynamic (SPH) method as a powerful Lagrangian method in modeling free surface flows is based on particle methods and can be used for modeling large deformation of surface boundary. This model has been modified via considering bed friction force and it is applied in this study to evaluate wave run up values. Two modifications i.e. stepped and smoothed approaches are introduced to implement bed shear stress in weakly compressible SPH models. Dam break flow and wave run up over different beach slopes are modeled and the results are compared with experimental and analytical data. It is concluded that considering the bed friction force is less important in dam break flows than in wave run up models that neglecting bed shear stress as a common practice in SPH methods can generate significant errors. These errors can be diminished efficiently by means of the introduced methods. The improvement rate, however, depends on slope geometry as well as wave condition and it is more sensible in simulating sliding waves over bed slope during run up phenomenon than breaking waves with considerable wave momentum. In the latter case, the wave momentum dominates the process and the bed friction force is not able to resist against the wave force and the the wave profile is consequently less dependednt on the bed friction value. By the way, the reslts have been yet improved and 40% error has been decreased to 7% in this case. In the former case with the limited wave run up values, however, the improvement is more noticeable and 90% error of the unmodified methods has been decreased to 6% using the modified SPH method. The results show that the wave run up will be modified using the bed friction force. Meanwhile, both the introduced method i.e. smoothed and stepped exertion of bed friction forces, results in nearly same wave profile because the total force is equal in both schemes. The only difference is the distribution pattern of the force between particles located near the friction boundary that leads to different distribution of particle velocities. Smoother velocity profile can be resulted in case of using transitional application of bed shear force which is moe comtaible with the natue while the stepped insertion of bed friction force may lead to numerical errors too. In spite of better result of the smoothed method, the implementation of the stepped method is easier and needs less numerical efforts. In addition, parallel processing using graphical processing units (GPU) are utilized to increase the efficiency of the modified model. The efficiency of GPU in comparison with CPU is evaluated and computational costs of different numerical steps are analyzed. It is observed that calculation of forces is the main time consuming step and using GPU can speed up the modified model significantly