A decoupling numerical method for fluid flow

A first‐order non‐conforming numerical methodology, Separation method, for fluid flow problems with a 3‐point exponential interpolation scheme has been developed. The flow problem is decoupled into multiple one‐dimensional subproblems and assembled to form the solutions. A fully staggered grid and a conservational domain centred at the node of interest make the decoupling scheme first‐order‐accurate. The discretization of each one‐dimensional subproblem is based on a 3‐point interpolation function and a conservational domain centred at the node of interest. The proposed scheme gives a guaranteed first‐order accuracy. It is shown that the traditional upwind (or exponentially weighted upstream) scheme is less than first‐order‐accurate. The pressure is decoupled from the velocity field using the pressure correction method of SIMPLE. Thomas algorithm (tri‐diagonal solver) is used to solve the algebraic equations iteratively. The numerical advantage of the proposed scheme is tested for laminar fluid flows in a torus and in a square‐driven cavity. The convergence rates are compared with the traditional schemes for the square‐driven cavity problem. Good behaviour of the proposed scheme is ascertained.