A Characteristic-based Split Finite Volume Algorithm for the Solution of Incompressible Flow Problems

The characteristic-based split (CBS) method has been widely used in the finite element community to facilitate the numerical modeling of the Navier-Stokes equations. In this paper a CBS-based finite volume algorithm is introduced for the solution of incompressible Navier-Stokes equations. The proposed method is implemented on a co-located grid arrangement and employs a transient fractional step method. In the first step, an explicit characteristic-based method is employed to obtain an intermediate velocity field from the modified momentum equations. Using continuity as an equation for pressure, the divergence-free velocity constraint of incompressible flow is also enforced in the second step. To devise a fully explicit algorithm for the solution of the pressure equation, an artificial compressibility factor is also defined and used. The correct, divergence-free velocity field is calculated afterwards using the intermediate velocities and the pressure field. Explicit time iterative solution of the finite volume algorithm discussed above is subjected to time step limitations. To validate the proposed CBS finite volume method, computational results are compared to those of numerical and experimental benchmark solutions. Satisfactory convergence rates and accurate results are obtained in all steady state and transient test cases.