A Linearized and Segregated Variational Multiscale Method for Incompressible Flows

The variational multiscale (VMS) method is recognized for its effectiveness in simulating turbulent incompressible flows due to its robust handling of scale interactions. However, traditional VMS approaches require solving strongly coupled nonlinear velocity–pressure systems, leading to significant computational challenges, especially regarding memory consumption and solution time. To overcome these limitations, a linearized and segregated VMS (LS-VMS) formulation is proposed, where velocity and pressure systems are decoupled and linearized, substantially reducing computational complexity. Numerical tests conducted include two-dimensional and three-dimensional Taylor–Green vortex flows, lid driven cavity flow, and the flow around NACA0012 airfoil for different angles of attack. Results illustrate notable performance improvements: When compared to the fully coupled VMS method, RAM usage is reduced by up to 70%, and (Formula presented.) computational speed-ups are achieved. The segregated formulation enables more effective preconditioning of the linear sub-problems. Importantly, the LS-VMS formulation has accuracy close to that of DNS reference solutions as the mesh is refined.