Orthogonal Collocation on Finite Element Method for Lid-Driven Cavity Flow

Abstract

Among the candidates for the Electrical Energy Storage (EES), Redox Flow Batteries (RFBs) are drawing attention towards a feasible solution. They are advantageous in flexibility and long-term stability of capacity and are therefore expected to play a critical role in the renewable energy and microgrid system. Meanwhile, the performance of the RFBs greatly depends on the motion of the electrolyte. And the problem becomes more complicated when we consider the edge effect in 2-dimensional modeling. Up to date, there is no analytical solution for the fluid dynamics of electrolyte flow in RFBs. To maximize the performance and enable optimum real-time battery management, fast and robust algorithm for the flow model and numerical simulation in multi-dimension is essential. In this presentation, we introduce Orthogonal Collocation on Finite Element (OCFE) approach in the successive domain for the classical 2-D lid-driven cavity flow problem. The Navier-Stokes equation is mathematically reformulated as Partial Differential Equations (PDE) of stream function and vorticity. To get the vorticity boundary condition, imaginary points, which are located at the outside of the cavity boundary, are introduced. The result shows good agreements with precedential values while using minimum computational time and memory.