Continuum methods have been used for numerical simulation of solid and fluid for a long time but they have several constraints. For complex fluids, numerical simulations using continuum assumptions are very challenging especially when the phenomena occurring in the system are smaller than the continuum — limit below which fluid cannot be considered as a continuum. Thermal fluctuation (due to Brownian motion) become significant at micro and nanoscale. As a result, continuum methods are not directly applicable at these scales. On the other hand, when the continuum simulations work for simulations at other scales, they have an additional challenge (especially in structural dynamics simulations). When the dynamics of the solid simulations are extreme and high deformations occur in the system, the continuum methods that are based on the idea of small element/mesh fail. Generating a mesh, that can be adequate to the dynamics is very difficult and still one of the big challenges of the continuum simulations. Even if a high-quality mesh is generated, a severe mesh distortion may occur for certain dynamics. In those cases, it is important to remesh the system. Thus, having a good quality mesh is not enough, the meshing process should also be extremely fast. Furthermore, the frequency of remeshing depends on the quality of the mesh, so there needs to be a balance of quality and efficiency. In fluid simulations, most continuum methods are based on the Eulerian approach of the flow field, i.e. system is studied by dividing into small elements/mesh (typically fixed) and fluid motion is studied through those points. In the Lagrangian specification of the flow field, fluid is assumed to be made of small particles. These particles are then tracked throughout the simulation to study the system behavior. These second methods of simulating fluid/solid fall into a general class called Particle methods. There are several kinds of particle methods such as Brownian Dynamics, Smoothed Particle Hydrodynamics, and Dissipative Particle Dynamics(DPD) that vary from each other on length scale, time scale, and model but have some similarities. Particle methods are very powerful and can be used to solve the challenges that are faced in the continuum method. In this dissertation, two problems that are encountered in simulating fluid and solid are tackled and solutions are proposed.
In simulating fluid using particle methods such as DPD, two major problems occur. First, particle density fluctuations near the solid-liquid interface, and second high computational cost due to solid wall. Particle density in DPD is defined as the local density of the particle. Density fluctuations occur due to the low solid wall particle density. One way to tackle it is increasing the solid wall particle density but that results in even higher computational cost. In this dissertation, first modified version of DPD — multibody Dissipative Particle Dynamics(MDPD)— is chosen due to its capability of handling the free liquid surface. In the context of MDPD, a closed-form mathematical framework is developed to model the solid wall and the original particle wall is replaced by this proposed model. The model is derived using a modified conservative force and a combination of analytical and numerical integration. The wall model is simpler and computationally efficient than traditional approaches of modeling the wall. The proposed wall model is also capable of mimicking the high-density computational wall that results into extremely low (less than 1%) density fluctuations. Furthermore, another challenge in MDPD and particle method community, a discrepancy in wall density is also solved by normalizing the wall density with fluid density. Several examples of fluid-solid interaction are used and the superiority of the wall boundary model is demonstrated. Computational time using wall model is only 30% − 50% of the computational time using the traditional particle wall. A dynamic case of solid sphere transport inside a water droplet due to wettability gradient is also demonstrated. In that example, several parametric studies such as the effect of wettability gradient, droplet radius and solid sphere radius is studied. The proposed wall model can easily be extended to other particle-based methods such as SPH and density fluctuations can be reduced. Furthermore, lower computational time will enable to simulate larger systems for longer times.
In solid mechanics and structural dynamics simulation, there are three steps, pre-processing(creating the geometry and mesh), numerical simulation, and postprocessing (analyzing the results from obtained data). Mesh generation is one of the critical stages in numerical simulation and it is still very challenging depending on the geometry and mesh requirement. The process of mesh generation becomes even more challenging when there is high deformation physics. In those cases, the mesh needs to be of high quality and sometimes even after that, remeshing is required. In this dissertation, a novel, simple and efficient model based on the particle method for isotropic unstructured mesh generation is proposed. The proposed method uses simple point particles with varying cutoff radii and densities. The cutoff radii dictate which surrounding particles exert force on the particle. Several force models are also proposed that affect the convergence speed and accuracy of the system. The mesh generation process follows these steps. First, a target number density of the particles is defined based on the desired refinement in the system. Next, a total number of particles is calculated which is a function of density contour and the system volume. The system is then filled with particles randomly and is set to reach equilibrium. Furthermore, several numerical schemes such as implicit and semi-implicit, and their effect on convergence speed and accuracy are also described. A Voronoi-Tessellation-Delaunay-Triangulation(VT-DT) is developed for two dimensions and three dimensions. VT-DT is used to create mesh from the particle position. The obtained mesh consists of triangular (two dimensions) and tetrahedral (three dimensions) elements. This proposed mesh generation method achieves higher mesh qualities than do its counterparts in prior works. For the mesh, several 2D and 3D benchmark cases are used to demonstrate the capability of the proposed method. Some non-engineering mesh examples are also demonstrated to showcase the robustness of the method. The proposed mesh generation model is simple, efficient, and can be used to generate mesh for any geometry and any level of refinement. Furthermore, the speed of the mesh generation enables this method to be used on applications where remeshing is needed.
