Stability and Accuracy of Mesh-free Particle Methods for Free-surface and Multiphase Flows

The main objective of the current Ph.D. thesis is to enhance consistency and accuracy of two of the most widely used mesh-free Lagrangian particle methods namely Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-implicit (MPS) models for simulating a wide range of multiphase flows and convection-diffusion problems involving heat and mass transfer. To this end, four different high-order gradient and Laplacian operators are first derived from the Taylor series expansion in both SPH and MPS contexts and are then employed for the discretization of diffusion terms, Pressure Poisson's equation (PPE), and divergence of velocity in governing equations. In order to retain the overall accuracy of the solution, a novel hybrid predictor-correction solution algorithm is first developed based on the combination of the explicit Third-order TVD Runge-Kutta scheme and two-step projection model and then is employed for the treatment of the transient terms in the Navier-stokes and energy equations and also handling the pressure-velocity coupling between the mass and momentum equations. To enhance the stability of the models, a novel particle regularization scheme so-called Particle Shifting Technique (PST) is introduced in the context of the MPS model and is then applied to circumvent the shortcoming associated with particle clustering/bunching in the Lagrangian framework.