Locally implicit hybrid algorithm for steady and unsteady viscous flows

A locally implicit hybrid finite volume algorithm on mixed type of triangular and quadrilateral meshes for the two-dimensional steady and unsteady viscous flows has been developed. The unsteady, full Navier-Stokes equations are solved in the Cartesian coordinate system. A new construction of a total-variation-diminishing formulation on triangles is used to obtain high-resolution results in the convective-dominated flow region. In the viscous-dominated part, a second- and fourth-order dissipative model on quadrilateral grids is employed to minimize the numerical dissipation