STABILITY OF THE THREE-STEP SPLITTING SCHEME FOR THE NAVIER-STOKES EQUATIONS IN THE CONTEXT OF THE LARGE PARTICLE METHOD - Tamabay, Д.; Zhumagulov, Б. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2024)
In this study, the issues of stability of "large particle" type difference methods for the Navier-Stokes equations are analyzed. A modified approach is proposed in the form of a three-step splitting scheme for physical processes, which differs from the classical scheme by using implicit difference schemes at the first and second stages. It is shown that this approach is effective for numerical implementation and provides a priori estimates of the second derivative of the velocity vector and pressure gradient, which ensures the stability of the scheme. Estimates of the stability of the proposed scheme are obtained, and the corresponding theorem is formulated. The results of the study emphasize the importance of the proposed approach for more accurate numerical modeling of various physical processes. The considered modified splitting scheme for physical processes for the Navier-Stokes equations can be applied for various computational experiments and for modeling physical processes.