In the paper the task of real-time synthesis of quality images of resulting data obtained in simulation of unstable oil displacement from porous media is considered. A new, GPU-based method to construct and visualize on UltraHD screens a polygonal model of the isosurface of the saturation of displacing liquid was proposed. The method is based on distributing and parallelizing of «marching cubes» threads between GPU cores by means of programmable tessellation. As initial graphic primitives, quadrangular parametric patches are used, the processing of which on the GPU is high-performance and has low video memory overhead. The proposed method was implemented in visualization software and successfully tested. The proposed solution can be used in researches in oil and gas industry as well as in virtual environment systems, virtual laboratories, scientific and educational applications, etc.