Split, characteristic based semi‐implicit algorithm for laminar/turbulent incompressible flows

In an earlier paper, Zienkiewicz and Codina (Int. j. numer. methods fluids, 20, 869–885 (1995)) presented a general algorithm for the solution of both compressible and incompressible Navier–Stokes equations. The algorithm, based on operator splitting, permits arbitrary interpolation functions to be used while avoiding the Babŭska–Brezzi restriction. In addition, its characteristic based approach introduces a form of rational dissipation. Zienkiewicz et al. (Int. j. numer. methods fluids, 20, 887–913 (1995)) presented the application of this algorithm in its fully explicit form to various inviscid compressible flow problems. They also presented two incompressible flow problems solved by the fully explicit form, employing a pseudo compressibility. The present work deals with the application of the above algorithm it its semi‐implicit form to some incompressible flow benchmark problems. Further, it extends the methodology to turbulent flows by employing both one, and two equation turbulence models. A comparison of results with earlier investigations is presented. Other issues addressed in this study include the effect of additional diffusion terms present in the scheme for both laminar and turbulent flow problems and some practical difficulties associated with local time stepping

Shock capturing viscosities for the general fluid mechanics algorithm

The performance of different shock capturing viscosities has been examined using our general fluid mechanics algorithm. Four different schemes have been tested, both for viscous and inviscid compressible flow problems. Results show that the methods based on the second gradient of pressure give better performance in all situations. For instance, the method constructed from the nodal pressure values and consistent and lumped mass matrices is an excellent choice for inviscid problems. The method based on L2 projection is better than any other method in viscous flow computations. The residual based anisotropic method gives excellent performance in the supersonic range and gives better results in the hypersonic regime if a small amount of residual smoothing is use

A general algorithm for compressible and incompressible flow—Part II. tests on the explicit form

The algorithm introduced in Part I of this paper is applied in its explicit form to a variety of problems in order to demonstrate its wide range of applicability and excellent performance. Examples range from nearly incompressible, viscous, flows through transonic applications to high speed flows with shocks. In most examples linear triangular elements are used in the finite element approximation, but some use of quadratic approximation, again in triangles, indicates satisfactory performance even in the case of severe shocks