An upwind compact difference scheme for solving the streamfunction–velocity formulation of the unsteady incompressible Navier–Stokes equation

Development of a Fourier‐expansion based differential quadrature method with lattice Boltzmann flux solvers: Application to incompressible isothermal and thermal flows

“…Two Reynolds numbers, that is, $$$ \mathit{\operatorname{Re}}=1{0}^3 $$$ and $$$ 1{0}^4 $$$, are simulated in the present work to test the accuracy and stability of the LBFS‐FDQ method. To compare the present results with reference data in the literature, the $$$ \mathit{\operatorname{Re}}=1{0}^3 $$$ case are tested with $$$ w=80 $$$, $$$ \delta =0.05 $$$ and $$$ b=0.25 $$$, 26,29,30,14 whereas $$$ w=30 $$$, $$$ \delta =0.05 $$$ and $$$ b=0 $$$ are used for the $$$ \mathit{\operatorname{Re}}=1{0}^4 $$$ simulations 31–33 …”

“…To compare the present results with reference data in the literature, the Re = 10 3 case are tested with w = 80, 𝛿 = 0.05 and b = 0.25, 26,29,30,14 whereas w = 30, 𝛿 = 0.05 and b = 0 are used for the Re = 10 4 simulations. [31][32][33] The flow at Re = 10 3 is computed with the grid sizes of 31 × 31 and 51 × 51. The vorticity contours obtained by the present method at t = 1.0L∕U 0 and 1.5L∕U 0 are plotted in Figure 7.…”

Intelligent Design Optimization System for Additively Manufactured Flow Channels Based on Fluid–Structure Interaction

“…In the meantime, it is necessary that proper boundary conditions and the reference pressure are configured to activate the compressible flow simulation. At the beginning of the simulation, lower order discretization schemes, such as upwind differencing scheme [41] and the k-ε turbulence model for turbulent flow, should be preferentially selected if the iteration index is small or the simulation has convergence issues. With the increase of the iteration index, higher order advection schemes can be employed to improve the accuracy of simulation.…”

Square Cavity Flow Driven by Two Mutually Facing Sliding Walls

“…  ， with  the wave number. Square cavity flows driven by two or more walls have been considered in the literature to some extent [9][10][11][12][13][14]. Perumal and Dass [9] employed the lattice Boltzmann method to prove the multiplicity of stable steady solutions that arise when two adjacent walls move away from their connecting corner at equal speeds.…”

“…For the parallel sliding walls case, Lernee et al [11] found a similar result for the pitchfork bifurcation, but they extended the analysis to higher values of the Reynolds number and detected a Hopf bifurcation of the asymmetric state at 10750 250 H Re   . For the antiparallel case and using an upwind compact differences scheme applied to the stream function formulation, Yu and Tian [12] detected the steady state multiplicity and the pitchfork bifurcation at about the same value of the Reynolds number 3200 P Re  . Yang and Zhang [13] set the focus on the capability of the conservation-elementsolution-element (CE/SE) method for resolving both corner and off-corner vortices at low Reynolds numbers, they evaluated the flow inside the two-sided cavity with anti-parallel motion of the top and bottom walls.…”