1 The 5th International Conference on Engineering Mechanics and Automation (ICEMA 5) Hanoi, October 11÷12, 2019 Lagrangian Vortex Particle Method for Complex Flow Simulation Duong Viet Dunga,, Lavi Rizki Zuhalb and Hari Muhammadc a VNU-University of Engineering and Technology, 144 Xuan Thuy, Cau Giay, Vietnam, [email protected] b Institut teknologi Bandung, Bandung, Indonesia, [email protected] c Institut teknologi Bandung, Bandung, Indonesia, [email protected] Abstract In order to solve complicated simulation problem for complex deforming objects under complicated motions found in aerospace, aerodynamic, meteorology, biology engineering, this paper presents Lagrangian vortex method based on Brinkman penalization. The Brinkman penalization acts as an external force, which is implicitly enforced into Navier-Stokes equation in the velocity-vorticity form. The advantage of the method is the capability to remove the pressure factor which causes errors in other numerical methods due to the complexity of shape of the object. Furthermore, the method is able to model the complex geometry, complex motions as well as 3D deformation of the object. In particular, the Navier-stokes equation can be solved in a classical strategy: applying Bio-Savart law formula is to deal with the convection process; employing fast multipole method to accelerate the velocity computation. The convergence is verifed in several simulation applications such as air fow over low aspect ratio wing, rotation wings, infuent of wind gust on high-raised building, and fsh swimming. Key Words: brinkman penalization, vortex particle method, complex fow applications 1. Introduction Flow problems around complexs deformable bodies have attracted a lot of interest within this decade in Rasmusen (2008), Li et al (2012), Mattia et al (2011), Eric (2004). Predicting the fuid-structure interaction responses also plays an important role in order to avoid potential aero-elastic and hydro- elastic instability issues, or to enhance performance by adapting the structural confguration. However, conducting experiments to study the fow over deformable bodies are difficult, see Eric (2004). In addition, a distinguishing feature of deformable bodies in real fuids is the generation of vorticity and the shedding of vortices into the wake, which is 2 Hai Ngoc DUONG, Thang Tat NGUYEN and Trong Duy NGUYEN difficult to predict using analytical approach. Due to current development of high performance computers, these problems can be overcome using numerical methods known as computational fuid dynamics (CFD). In CFD, there are two main approaches: grid-based and meshless methods. As suggested by the name, in the more traditional grid-based methods, the Navier-Stokes equation is solved using discretized grid. However, simulation of fow over deformable body is very difficult, if not impossible, using the grid-based CFD. In particular, the difficulty is due to requirement to generate grid at every time step because of the continuous change in the geometry of deformable body. On the other hand, meshless methods, such as smoothed particle hydrodynamics (SPH) in Kajtar and Monaghan (2012) and vortex element methods in Barba (2004), Cottet and Poncet (2004), have benefted from their inherent adaptivity. Specifcally, the meshless or Lagrangian methods use Lagrangian grid points, which follow the movement of the fows. Therefore, such methods can handle irregular and complex geometries without any complication. As far as complex vortical fow is concerned, vortex element method is the suitable solver to resolve the vorticity region correctly with high resolution in Kamemoto (2004). In addition, another advantage of the method is that it can be easily implemented in parallel computation in order to allow long time simulation. Accordingly, the fully meshfree version of the vortex element method (VEM) is developed in this research in order to simulate the complex 3D fow problems. Fast Multipole Method (FMM) is employed to accelerate the computation of the developed VEM. A novel Brinkman penalization boundary condition is introduced to model the complex deformable geometries under its motions (translation and rotation). Finally, the performance of the developed method is investigated by performing benchmark bounded fow simulations ranging from aerospace engineering to biological engineering and wind engineering. 1.1. Vortex particle method The vortex methods are based on the momentum equa