Improving the Speed and Accuracy of Projection-Type Incompressible Flow Solvers

Selective edge removal for unstructured grids with Cartesian cores

“…The selective edge removal option was implemented in FEFLO, a general purpose edge-based finite element flow solver using linear elements [18], and was tested on a variety of examples, of which four are included here. We remark from the outset that the main aim of the comparison is the quality of the results as well as the relative speed of typical unstructured grids vs. those with Cartesian cores.…”

“…10(a). The incompressible Euler equations were solved using a projection scheme [18]. The advective fluxes, which are integrated explicitly, are built using upwind bias, gradient reconstruction and van Albada limiting [8].…”

Deflated preconditioned conjugate gradient solvers for the Pressure–Poisson equation

“…4(b)). The simulation was performed using implicit timestepping, solving a pseudo-steady problem at each timestep [27]. Within each pseudo-timestep the advective terms were integrated implicitly using 5 LU-SGS passes (local Fig.…”

“…boundary layer) grids [32,40] (in the sequel diagonal preconditioning is assumed to be the default for isotropic grids); -Multistage or implicit treatment of the advective terms (more advective-diffusive work, allowing larger timesteps, nearly the same work for the Pressure-Poisson equation) [25,27].…”

“…ð2Þ where q; v; p; l denote the density, velocity, pressure and viscosity of the fluid, are based on so-called projection techniques, whereby the advancement of the flowfield in time is split into the following three substeps [22,2,23,3,32,15,1,17,37,13,24,8,41,11,19,18,20,40,[25][26][27][28]:…”