In clinical diagnostics of the coronary artery stenosis, the state of fluid flow is analyzed by invasively measuring fractional flow reserve (FFR). However, a more detailed hemodynamic evaluation of the flow and its spatial and temporal distribution may be more insightful for the diagnostics. A realistic simulation of blood flow inside the patient-specific coronary artery could be a better alternative to the invasive measurement of FFR. In this study, lattice Boltzmann (LB) method was used for the simulations of fluid flow through complex geometries of human coronary arteries. For such complex geometries, a large number of nodes in the LB mesh are denoted as fixed and this imposes large computational and memory requirements that are unnecessary. In this study, this standard approach is improved by using a sparse domain that includes the fluid nodes and its closest fixed (solid) nodes. This way, the amount of required memory resources is significantly reduced. During implementation, the software is parallelized to execute on a GPU (graphics processing unit) device, ensuring that the amount of computational time needed for the execution of the simulation is also significantly reduced. The software presented in this paper provides a valuable tool that can be used in clinical practice for quick assessment of the state of the arteries and provide fast quantitative information about fluid flow that could be very useful for medical diagnostics and decision-making.