PENINGKATAN METODE VORTEX DENGAN MENGGUNAKAN PENALISASI BRINKMAN DAN SKEMA-SKEMA AKSELERASI - Xuan Canh, Cao
Today, computational fluid dynamics (CFD) methods have been used extensively for solving Fluid Mechanics, compared to the more expensive experiments. In CFD, the physical domain is discretized by using mesh/grid, cells, nodes or particles generation. However, the methods based on a grid are required to have high grid generation cost for complex, deforming, and moving bodies. The meshfree methods which established on particles are also met defective aspects, especially, solving N-body problems frequently requires O(N2) order of computational time. These may become computationally expensive. The improvement of acceleration method is one of the most important precondition to accelerate the computational time. Based on that, the finer resolution or higher order in some numerical procedure could be used to provide more accurate results without the higher expense. In this research, the Vortex-in-Cell (VIC) method and Vortex Element Method (VEM) as the members of the Vortex Method (VM) family will be elaborated. The hybrid VIC algorithm where the grid-based and meshfree method is combined as the blending algorithms particle-mesh/grid methods. The VIC interpolates the particle strength to an underlying mesh. This method has the advantage that the Poisson inversion can be accomplished and accelerated by the Fast Fourier transform techniques. The classical Vortex Element Method, Vortex Particle Method which employs Green’s function to solve the Poisson equation is accelerated as well, by using the Fast Multipole Method (FMM). Furthermore, the vorticity strength of particles will be diffused by diffusion modeling Particle Strength Exchange (PSE) which can be accelerated by utilization of the linked-list scheme. Boundary condition treatment is a problem for many researchers who are in charge of fluid flow past the immersed obstacle even in both grid-based or meshfree methods. In the long journey of seeking the boundary condition model to simulate the bounded flow, the existing higher order Brinkman penalization is applied into grid field of VIC method to overcome this difficulty. For particles of VEM, a new immersed boundary condition model is also developed, that based on Brinkman penalization for the enforcement of the no-slip boundary condition. In this research, numerical codes based on the VIC algorithm and VEM are developed. The performance of the method will be examined by solving several unbounded/ bounded flow for problems. The improvement of results has been achieved. For the last attempt of simulation the realistic problems which always stay on the high Reynold number region, we tried to develop Large Eddy Simulation (LES) schemes. By using LES, the expensive finer resolution can be replaced by acceptable resolution.