Solar wind streams, acting as background, govern the propagation of space weather drivers in the heliosphere, which induce geomagnetic storm activities. Therefore, predictions of the solar wind parameters are the core of space weather forecasts. This work presents an indigenous three-dimensional (3D) Solar Wind model (SWASTi-SW). This numerical framework for forecasting the ambient solar wind is based on a well-established scheme that uses a semi-empirical coronal model and a physics-based inner heliospheric model. This study demonstrates a more generalized version of Wang-Sheeley-Arge (WSA) relation, which provides a speed profile input to the heliospheric domain. Line-of-sight observations of GONG and HMI magnetograms are used as inputs for the coronal model, which in turn, provides the solar wind plasma properties at 0.1 AU. These results are then used as an initial boundary condition for the magnetohydrodynamics (MHD) model of the inner heliosphere to compute the solar wind properties up to 2.1 AU. Along with the validation run for multiple Carrington rotations, the effect of variation of specific heat ratio and study of stream interaction region (SIR) is also presented. This work showcases the multi-directional features of SIRs and provides synthetic measurements for potential observations from the Solar Wind Ion Spectrometer (SWIS) subsystem of Aditya Solar wind Particle EXperiment (ASPEX) payload on-board ISRO's upcoming solar mission Aditya-L1.