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 sche me 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 inte rest make the decoupling scheme first-order-acccurate. The discretizat ion of each one-dimensional subproblem is based on a 3-point interpola tion function and a conservational domain centred at the node of inter est. The proposed scheme gives a guaranteed first-order accuracy. It i s shown that the traditional upwind (or exponentially weighted upstrea m) scheme is less than first-order-accurate. The pressure is decoupled from the velocity field using the pressure correction method of SIMPL E. Thomas algorithm (tri-diagonal solver) is used to solve the algebra ic equations iteratively. The numerical advantage of the proposed sche me is tested for laminar fluid flows in a torus and in a square-driven cavity. The convergence rates are compared with the traditional schem es for the square-driven cavity problem. Good behaviour of the propose d scheme is ascertained.