Relativistic jets are widely observed in astronomical objects including active galactic nuclei and gamma-ray bursts. However, the acceleration mechanisms that drive these jets are not yet fully understood. Recent studies have shown that when a jet possesses an initial velocity corresponding to approximately 90% of the speed of light, it can be accelerated to a Lorentz factor of about 100 through expansion in the direction perpendicular to the jet's flow. Nevertheless, how such initial velocities are acquired remains unclear. In this study, we analyzed the acceleration process of relativistic hot gas ejected into a vacuum using a newly developed special relativistic Smoothed Particle Hydrodynamics (SPH) method. As a result, we successfully numerically reproduced the process by which stationary gas is accelerated to approximately 95% of the speed of light, following Bernoulli's principle. In this presentation, we will report on our research aimed at elucidating how relativistic hot gas is accelerated in a vacuum. In particular, we will clarify the essential role that the vacuum environment plays in the acceleration process and discuss the primary numerical challenges encountered. We will also describe the technical details of the relativistic SPH method developed in this study and present the obtained analytical results.