Numerical simulation of viscous flows in channels with a step

Coordinate Free Programming of Computational Fluid Dynamics Problems

“…This allows a wider window of stability above an explicit implementation and thus permits the use of practical working time steps [18,19,31]. Such advantages continue through to more complex non-Newtonian settings, where inertial influences via Reynolds number are low, in contrast to elastic effects (for further details see [22]).…”

“…A vector field is now approximated by u n ≈ mv j=1 U n j ϕ j and a scalar field by p n ≈ mp j=1 P n j ψ j , where the superscript n denotes evaluation at time step n, as before. The finite element interpolants are then substituted in Eqs (17)(18)(19)(20)(21) and appropriate test functions v and q chosen to produce a set of matrix equations.…”

“…This argument maintains the overall order of the scheme [31]. We shall see below, in the variational form of the problem, that natural homogeneous Neumann boundary conditions emerge from step 2 and these are a distinct advantage to this scheme [18,19].…”

“…where D is a chosen diagonal form and ω is a positive relaxation factor [19,10]. The direct Choleski method is employed to solve the pressure difference Eq.…”

Three-dimensional flow effects on forced convection heat transfer in a channel with stepwise-varying width

“…Regarding these configurations, a number of researchers [1][2][3][4] focused their investigations on the twodimensional characteristics of the separated flow, both in the laminar and the turbulent region, with the backward-facing step case to be considered as a benchmark problem for validating numerical codes [2].…”