Numerical algorithm based on regularized equations for incompressible flow modeling and its implementation in OpenFOAM

•QHD, or regularized hydrodynamic equations for viscous incompressible flow and associated numerical algorithm are described.•The semi-implicit approximation of QHD equations using finite volume method is implemented as an OpenFOAM solver QHDFoam.•The new algorithm has simple loop structure compared with PISO, SIMPLE and Chorin projection methods.•The QHD algorithm was verified with several flow modelling problems including forced and natural convection.•The convergence of QHD numerical algorithm to reference solution for the problem of internal gravity wave attractor was shown. Various aspects of incompressible viscous flow modeling using regularized equations are considered: from the formulation of quasi hydrodynamic (QHD) equations for fluid motion to the demonstration of the capabilities of the associated OpenFOAM solver QHDFoam. The numerical algorithm for fluid flow simulations is devised using the QHD approach. Unlike prominent operator splitting techniques (PISO, SIMPLE and their variants), the QHD approach provides an equation for pressure explicitly. Practical issues of QHD approximation and stability criteria for the numerical scheme are presented. Several problems are used to validate the developed solver and to demonstrate its capabilities: backward facing step, skewed cavity flow, natural convection and generation of internal gravity waves attractor. Results of simulations for the last case are obtained using 3 different methods to show peculiarities of the quasi hydrodynamic equations approach in comparison with the standard PISO algorithm and finite-volume method and with the solution based on the spectral element method. The source code of the developed OpenFOAM solver(s) can be downloaded from the GitHub repository: https://github.com/unicfdlab/QGDsolver.