Shock absorbers are crucial components of a vehicle's chassis, responsible for the trade-off between stability, handling, and passenger comfort. Their role is to filter the disturbances imposed to the vehicle body, typically by passive energy dissipation through hydraulic oil. The aim of this research paper is to investigate the physical behavior of an advanced automotive racing shock absorber, known as TTR, developed by Öhlins Racing AB. This goal is achieved by developing a detailed lumped parameter numerical model of the entire TTR suspension in the 1D simulation tool, AMESim. TTR features a through-rod piston design, fully adjustable high and low speed compression and rebound adjusters, and a gas reservoir. The developed numerical model is capable of capturing the physics behind the real shock absorber damping characteristics, under both static and dynamic conditions. In particular, the model is presented in two levels of progressive physical complexity, in order to improve the numerical predictions of dynamic damping characteristics. Several physical phenomena are considered, such as the dynamics of the hydraulic volumes, the static and viscous frictions and the pressure-induced elastic deformation of the solid boundaries. Model validation is discussed, based on different types of measurements for both the individual hydraulic components and the entire shock absorber model. The coupled hydraulic and mechanical modeling together with the measurement comparisons, thoroughly discussed in the paper, allows discovering the influence of each single component on the shock absorber static and dynamic performance.