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A Finite Volume method for 3-D unsteady Fluid flow Analysis using Bi-Conjugate Gradient Stabilized solver

Shihabudheen Kunnath , Ramarajan A

The fluid flow problems play a significant role in predicting and understanding the flow pattern in different flow processes. The three dimensional flow analysis is made using an unstructured finite volume technique. The space discretization is carried out using arbitrarily oriented tetrahedral elements. The cell-centered scheme, which is popular in Fluid Dynamics, is directly adopted here. A Least square based methodology is used for the derivative evaluation using cell-centre values avoiding the tedious reconstruction and Bi-Conjugate Gradient Stabilized (Bi-CGStab) method is used for the solution of the resulting system of linear equations. Combination of unstructured finite volume method along with the Bi-CGStab solver is first proved by applying it to the solution of an unsteady 3D convection diffusion equation. A Taylor based upwind scheme similar to that of Taylor Galerkin approach is used. This gives second order accuracy and results in a natural upwind term. After the Taylor series application the results are cast into the general divergence form so that the finite volume method can be applied directly. The stability of the solution is tried for various peclet numbers and found to be robust. The methodology is then extended to 3D Navier Stokes equations and the code is validated for the lid-driven cavity flow. The implicit solutions obtained for the Navier Stokes equation using Bi-CGStab method is found to save considerable amount of computation time