A stable and accurate convective modelling procedure based on quadratic upstream interpolation

A numerical method for solving the 3D unsteady incompressible Navier–Stokes equations in curvilinear domains with complex immersed boundaries

“…Approximate factorization methods, say such as that developed by Beam and Warming [23], require the evaluation of the Jacobian of the right hand side of Eq. (21). It is easy to see, however, that in the present case the calculation of the Jacobian could be very costly as it would require the evaluation of the Christoffel symbols, which is exactly what we tried to avoid in the first place by developing the hybrid staggered/ non-staggered grid approach.…”

“…Let us assume that the volume fluxes at their respective surface centers are known at a given time stepReconstruction of the Cartesian velocity components at the volume centers-(u r )i,j,k (r = 1, 2, 3) -is accomplished using the onedimensional QUICK [21] interpolation formula, which was also employed for the Cartesian mesh analogue of the method by Gilmanov and Sotiropoulos [1]. For example, the V 1 volume flux is calculated by interpolating along the ξ 1 direction as follows: assuming the grid volumes centers along i direction is numbered from 1, 2, … i max , (19) Similarly the V 2 and V 3 volume fluxes are determined by interpolating along their respective grid lines (j and k lines, respectively).…”

“…First, intermediate volume fluxes V q(*) that do not satisfy continuity are calculated by solving implicitly (see below for details) the following momentum equations at the surface centers (we shall denote this step as the momentum step): (21) where V q(n) represents the solution at time step n, and G q is the curvilinear gradient operator expressed as in Eq. (15).…”

Desenvolvimento da modelagem de turbulência e interação fluido-estrutura para as vibrações induzidas por vórtices de cilindro rígido.

“…As commented above, a collocated approach is used and thus the face values ought to be related to the cell center values and that is achieved by means of interpolation practices. In the calculations showed in this thesis, two types of interpolation practices are applied, namely the upwind differencing scheme and the Quadratic Upstream Interpolation for Convective Kinematics (QUICK), see Ferziger & Peric (2002), Leonard (1979).…”

“…Therefore a flux limiter was necessary to make sure that wiggles in the solution are avoided. The reader is referred to the work of Leonard (1979) for the background of such flux-limiting schemes.…”