Higher-order characteristics-based method for incompressible flow computation on unstructured grids

An algorithm for numerical simulation of incompressible flows on three-dimensional unstructured grids is presented. It is an upwind finite volume method based on the method of characteristics, which is made possible with the introduction of Chorin's artificial compressibility formulation (Chorin, A., "A Numerical Method for Solving Incompressible Viscous Flow Problems," Journal of Computational Physics, Vol. 2, No. 1,1967, pp. 12-26). Flow variables are calculated along characteristics, and their initial values are interpolated based on the signs of the corresponding characteristics. In addition, an upwind-biased interpolation method of third-order accuracy is used for interpolating flow variables on unstructured grids. With these inherent upwinding techniques for evaluating convection fluxes at control volume surfaces, no artificial viscosity is required. The discretized equations are solved by an explicit multistage Runge-Kutta time-stepping scheme, which is found to be efficient in terms of CPU and memory overheads. A computer code has been developed using the numerical methods presented. A number of test cases, including two-dimensional/three-dimensional inviscid and viscous flows, have been calculated to validate the code and to evaluate the performance of the numerical algorithm. Numerical results obtained are in good agreement with exact solutions and other published experimental/numerical results. The convergence rate of numerical simulation is generally found to be satisfactory. The third-order characteristics-based scheme is found to be more accuarate than the second-order central scheme.