شبيه‌سازي محيط‌هاي چند فازي با استفاده از روش تركيبي BPM-SPH

در مقاله پيش رو نرم‌افزار كوانتا، كه توسط نويسندگان در حال توسعه است، معرفي و راستي آزمايي شده است. اين نرم افزار با اهداف پژوهشي و به منظور شبيه‌سازي دو بعدي محيط‌هاي چند فازي جامد و سيال و به زبان Visual C++ نوشته شده است. در اين نرم افزار محيط جامد با استفاده از روش مبتني بر ذره Bonded Particle Method و محيط سيال با استفاده از روش مبتني بر ذره Smoothed Particle Hydrodynamics شبيه‌سازي مي‌شوند. رفتار نهايي مدل حاصل اندركنش ذرات با ديگر ذرات همنوع خود و نيز ذرات متعلق به روش ديگر است. ابتدا درباره تئوري روش‌ها و نحوه استفاده از آن‌ها در نرم‌افزار توضيح داده شده و در انتها چند مسئله معيار به منظور راستي آزمايي نرم‌افزار مدلسازي و تحليل شده و نتايج شبيه‌سازي با نتايج موجود در مقالات مقايسه شده‌اند. براي راستي آزمايي روش ‌BPM از شبيه‌سازي تغيير شكل يك تير طره و براي راستي آزمايي روش SPH از شبيه‌سازي مسئله جريان حفره‌اي و نيز جريان پوازي استفاده شده است. براي راستي آزمايي محيط دوفازي و اندركنش بين ذرات BPM و SPH از مدل‌سازي يك سيلندر جامد در مسير جريان استفاده شده است. بررسي نتايج شبيه‌سازي‌ها نشان دهنده تطابق مناسب آن‌ها با نتايج تحليلي و تجربي موجود است.

The precision and speed of numerical simulations of physical phenomena has led to their increasing use in designing and research applications. These precision and speed are owed to the improvements in numerical methods and significant advancements in computing power of CPUs and GPUs. Particle-based methods are some of the most recently developed numerical simulation methods. Development of these methods has been long delayed due to the need for a relatively high computational effort. Particle-based methods can be considered as a subset of Meshless Methods. In nonlinear computational methods, mathematical equations in the problem domain are estimated only by nodes, and contrary to the case about the nodes in FEM and FDM methods, there is no need for these nodes to be connected to each other by a mesh. If the nodes are particles that carry physical properties, such as mass and stiffness, and simulations proceed on the basis of updating trajectory and physical properties of particles, then the method is called a particle-based method. Particle-based methods include molecular dynamics (MD), Discrete Element Method (DEM), Smoothed Particle Hydrodynamics (SPH), and Lattice Boltzmann Method (LBM). The number of studies and computer codes developed based on these methods has grown dramatically over the past two decades. Among particle-based methods, DEM method is mainly used to model solid objects and fractures and in some cases it has been used to model granular materials like soil. While most of the applications of SPH method include numerical solution of the Navier-Stokes equations in fluid dynamic problems. Despite their differences, both DEM and SPH methods are particle-based methods and so there have been successful attempts to integrate them into a single application. In current study, a computer code called “QUANTA” is introduced. In this software, the researchers have tried to integrate the SPH method with another particle-based method called Bonded Particle Method (BPM). BPM is based on DEM and was originally developed to model rock and soil mechanics phenomena. QUANTA is being developed with the goal of providing a tool to simulate two-dimensional solid, fluid, and multi-phased interactive environments for research purposes. In this software, the solid environment is modeled using the BPM algorithm and the fluid environment is modeled using the SPH algorithm by solving Navier-Stokes equations. Depending on the problem at hand, BPM and SPH particles interact with each other by equations based on momentum or pressure. The code is developed using Visual C ++ programming language and has the ability to perform parallel computations with a remarkable speed. To verify the software, a few simple and frequently used problems in the literature were chosen. A cantilever beam was modeled and loaded to verify BPM part of the software. Poiseuille and shear cavity problems were used to verify the SPH part. In order to verify the interaction of these two algorithms, a solid cylinder was modeled once in a wind tunnel travelling at supersonic speeds and then against the flow of a viscous fluid. According to the results of these numerical modellings, the software can be deemed successful in simulating the sample problems. While simulation with particle methods requires more computational effort than common methods such as finite element and finite difference, the particle-based and micromechanical nature of these methods and their ability to model large-scale deformations and complex behaviors has, in many cases, made them logical choices for simulation. As the next steps of this study, the authors are developing new equations for interaction of particles and equations of state to improve the software performance.