Granular flows are commonly encountered in various engineering fields and industrial applications like silo/hopper discharge, rotating drums, pneumatic conveyors, fluidized beds and others. Unfortunately, the underlying physics in such processes is still poorly understood. Better understanding of these fundamentals is essential for design and optimization of such processes. The Discrete Element Method (DEM) and coupled Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) have become promising and efficient tools for modeling dry and multiphase flows, respectively. In DEM, a granular material is represented by a system of distinct interacting particles, while in CFD-DEM the physics of both the solid and fluid phases is taken into account. Traditionally, the majority of scientists and researches model dry granular and multiphase flows assuming particles as perfect spheres. Spheres are easy to handle in DEM and CFD-DEM codes and thus remain popular as particle representation method because of their simplicity and computational efficiency. Moreover, the contact models and drag correlations for such particles are well known and established. However, in real systems, which often consist of irregularly shaped particles, this assumption can be applied only to a limited degree. Usually, irregular particles can frequently be idealized by some regular shapes like superquadrics. The superquadric shape can be considered as an extension of spherical or ellipsoidal particles and can be used for modeling of spheres, ellipsoids, cylindrical and cuboidal particles with rounded corners by varying only five shape parameters. The main aim of the thesis is to implement computationally efficient realization of superquadric particles in open-source software packages LIGGGHTS (DEM) and CFDEMcoupling (CFD-DEM). The first part of the thesis gives a short introduction to DEM and a review of the most popular shape descriptors used by researchers in literature. Next, it provides the mathematical background of superquadric DEM along with a series of validation test cases. The simulation results obtained with the supequadric DEM are in good agreement with data available in literature. Further, the behaviour of superquadric particles at different blockiness/edge sharpness levels and multi-spheres with different numbers of sub-spheres (surface bumpiness) is compared on micro and macro level tests. Additionally, the effect of the overlap model for superquadric particles is studied and a time step criterion for superquadric DEM is proposed. It is shown that superquadric particles demonstrate an excellent trade-off between model complexity and shape flexibility. They are able to capture many effects of real particles and extend the range of applicability of DEM. The second part of the thesis is dedicated to non-spherical and, in particular, superquadric particles in CFD-DEM. Here, the two main approaches for modelling multiphase flows are discussed briefly: resolved and unresolved CFD-DEM. In the first approach, namely resolved CFD-DEM, the particles are considered to be significantly larger than the CFD cells, allowing to resolve the fluid flow around a particle in great detail.Two implementations available in the CFDEM(R)coupling (CFD-DEM) software, namely the Fictitious Domain and the Hybrid Fictitious Domain-Immersed Boundary Method (HFDIBM) are discussed and their adaptation for superquadric particles are presented. For the second approach, namely unresolved CFD-DEM, used when the particle diameter is much smaller than the CFD mesh size, a brief introduction is given and existing drag models for spherical and non-spherical particles are reviewed and validation test cases for superquadric particles are provided. Finally, the drag, lift and torque coefficients for the special case of cylindrical particles represented as superquadrics are studied. An accurate estimation of hydrodynamic torques as well as drag and lift forces on non-spherical particles is a fundamental problem in CFD since these have a strong dependency not only on the Reynolds number but also on the aspect ratio and particle orientation with respect to the flow direction. Only few insights could be found for an appropriate drag correlation for non-spherical particles. For this purpose, a series of simulations of uniform flow past a single static particle were conducted using the novel HFDIBM solver, varying incidence angle (angle of attack), Reynolds number andsuperquadric blockiness. The proposed methodology does not require domain re-meshing if particle shape or orientation of a particle with respect to the flow direction is changed. It can be applied to other particle shapes like prolate or oblate cuboids. The superquadric shape model was implemented in the open-source software packages LIGGGHTS and CFDEMcoupling. Superquadric particles are available in LIGGGHTS-PUBLIC for public download and expected to become part of CFDEMcoupling-PUBLIC by end of 2018.