Artificial Compressibility 3-D Navier-Stokes Solver for Unsteady Incompressible Flows with Hybrid Grids

Abstract

An unsteady incompressible numerical method for the solution of Navier-Stokes equations is presented. The finite volume solver adopts the method of artificial compressibility, using an implicit dual time stepping scheme for time accuracy. The 2D solver operates on general hybrid meshes containing triangles and quadrilaterals, while the 3D solver operates on hybrid meshes containing tetrahedra, pyramids, prisms and hexahedra. The developed algorithms for spatial discretization and time integration are mesh transparent. An upwind spatial discretization scheme is used for the convective terms and a central scheme for the diffusive terms. Efficient calculation of flow fluxes is implemented in an edge-wise fashion. A new combined method for efficient and accurate evaluation of variable gradients is achieved by using an averaging technique and by avoiding multiple spatial integration of the same element of the mesh. The results obtained agree well with numerical solutions obtained by other researchers.

Development and validation of an incompressible Navier-Stokes solver including convective heat transfer

“…Today, hybrid meshes are widely used (Anderson et al, 1995;Haselbacher and Blazek, 2000;Kallinderis and Ahn, 2005;Vrahliotis et al, 2012;Stokos et al, 2012Stokos et al, , 2013a. The hybrid meshes can combine good viscous layer resolving capability obtained from their structured elements, with the geometric flexibility of unstructured meshes (Kallinderis and Ahn, 2005).…”

“…A CPU-time efficient and mesh transparent method is used for the calculation of these gradients. This method was proposed by Vrahliotis et al (2012) for the Navier-Stokes equations and is implemented for the energy equation successfully. Cell gradients are first evaluated using Green's theorem.…”

MAST-RT0 solution of the incompressible Navier–Stokes equations in 3D complex domains

“…Several numerical procedures can be distinguished in the segregated approach, e.g. the projection method (Chorin, 1968;Kim & Moin, 1985), the penalty method (Braaten & Shyy, 1986;Hughes et al, 1979), the artificial compressibility method (Harlow & Welch, 1965;Malan et al, 2002;Vrahliotis et al, 2012), and the pressure-correction method (Ozoe & Tao, 2001;Patankar, 1980). The fractional step projection method (Chorin, 1968;Kim & Moin, 1985) and the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) pressurecorrection method (Patankar, 1980(Patankar, , 1981 have become very popular.…”

A cost-effective FE method for 2D Navier–Stokes equations

“…The system of equations is made up of the momentum equations and the incompressibility relation, and it is well known that the main difficulties in its solution reside in the approximation of the convective term and in the calculation of the pressure. A large amount of numerical methods have been developed particularly in the framework of finite elements (FE) (Baker, Dougalis, & Karakashian, 1982;Choi, Choi, & Yoo, 1997;Codina & Soto, 2004;Plana Fattori, Chantoiseau, Doursat, & Flick, 2013;Sun, Zhang, & Ren, 2012), of cell-centred finite volumes (Deponti, Pennati, & De Biase, 2006;Feraudi & Pennati, 1997;Kim & Moin, 1985;Pai, Prakash, & Patnaik, 2013) or cell-vertex finite volumes (Hookey & Baliga, 1998;Malan, Lewis, & Nithiarasu, 2002;Tritthart & Gutknecht, 2007;Vrahliotis, Pappou, & Tsangaris, 2012) and finite differences (Ali, Fieldhouse, & Talbot, 2011;Kumar, Dass, & Dewan, 2010;Shih & Tan, 1989). In the finite difference (FD) and finite volume (FV) *Corresponding author.…”