An efficient computational method for simulating incompressible fluid flows on a virtual cubic surface

Abstract

We propose an efficient computational algorithm for simulating incompressible fluid flows on a virtual cubic surface. By neglecting the influence of gravitational force, we effectively eliminate its impact on the system. Therefore, the dynamics can be characterized as essentially two-dimensional (2D) and confined to a plane. A projection method and a finite difference method (FDM) are used to numerically solve the Navier–Stokes (NS) equations governing the fluid flow. In the projection method, we need to solve the Poisson equation for the pressure field, which is effectively solved using a multigrid method. The multigrid method is a powerful computational approach that optimizes the solution process by using a hierarchical grid structure. The multigrid method allows efficient and accurate calculations of pressure values and increases the overall simulation accuracy and performance. The effectiveness of the proposed numerical algorithm is demonstrated through computational results of the shear flow and multi-vortex problems on a virtual cubic surface. These computational results validate the reliability and efficiency of the proposed approach, and therefore demonstrate its potential to contribute significantly to the field of computational analysis in fluid dynamics on a virtual cubic surface.