Smectics are typical layered phases of liquid crystals, which possess both orientational order and a periodic modulation of the center-of-mass density in the form of layers. They are of great interest in mathematics for the questions arising in their modeling and analysis. In this talk, we propose a new continuum model, solving for a real-valued smectic order parameter for the density variation and a tensor-valued nematic order parameter for the director orientation. The model is challenging to discretise due to the high regularity of the density variation; to address this, a continuous interior penalty discretisation is employed. Numerical analysis and experiments are performed to confirm the effectiveness of the proposed model and discretisa tion. The model numerically captures important defect structures in focal conic domains and oily streaks. Finally, we explore the topological configurations on button-like confinements by means of real-space microscopy experiments of hard rods and two other complementary theories: Monte-Carlo simulation and density functional theory. This yields a consistent description of defect structures on a qualitative level.