An Efficient Mesh-Free Particle Method for Modeling of Free Surface and Multiphase Flows

Numerical methods have been used extensively in modeling of free surface flows. These methods are generally classified into two categories; grid methods, and particles methods. In recent years, particle methods are gaining further attentions among numerical model developers for simulation of free surface flows. Computer simulation using particles has the capacity to analyze more complex geometry and physics than grid methods. Particularly, topological deformation of the fluid can be analyzed efficiently by particles, while it is hard and sometimes not possible to fit and move a grid continuously in such domains. Also, convection is directly calculated by the motion of particles without numerical diffusion. In addition, grid generation which recently seems to be used to analyze complex domains is not necessary, eliminating a significant portion of computational time. Although it is necessary to initialize configurations of particles in particle methods, this is much easier than grid generation as there is no need to set up topological relations among the particles. Problems with severe and sharp changes of free water surface can be simulated successfully with numerical methods based on the Lagrangian approach.;In this research the development of a numerical method based on the Lagrangian formulation to solve the Navier-Stokes equations is reported. Navier-Stokes equations are the governing equations of the fluids; a set of coupled partial differential equations that describe how the density, pressure, and velocity of a moving fluid are related. The Navier-Stokes equations are solved by the Moving Particle Semi Implicit (MPS) method, a mesh-free particle method. A fractional step method is applied which consists of splitting each time step in two steps. The fluid is represented with particles, and the motion of each particle is calculated based on the interactions with the neighboring particles covered by a kernel function.;In general, the contributions of this research can be categorized into three distinct parts: 1. Application of the MPS method is shown through the successful simulation of two sample complex free surface flows. Compared to the similar former studies focused on the application of this method, this research implements a newly-introduced kernel function. It is shown that by utilizing this new kernel function the stability of the simulations is significantly enhanced. 2. A multiphase MPS method is proposed for incompressible flows. The multiphase system is treated as a multi-density multi-viscosity fluid. A single set of governing equations is solved on the whole computational domain, and high-order accurate density and viscosity schemes are applied to stabilize the fluid pressure and shear stress fields. The proposed method is utilized for modeling of granular flows and sediment transport. 3. An algorithm is introduced to enhance the efficiency of the mesh-free particle methods. This algorithm enables the implementation of sets of particles with different sizes in one computational domain.