A new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya-Babuška-Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie-Chow interpolation or by using a Petrov-Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes, and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2. ≤. CFL≤. 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.
Christon, M. A., Bakosi, J., Nadiga, B. T., Berndt, M., Francois, M. M., Stagg, A. K., … Luo, H. (2016). A hybrid incremental projection method for thermal-hydraulics applications. Journal of Computational Physics, 317, 382–404. https://doi.org/10.1016/j.jcp.2016.04.061