Numerical simulation of bubble rising in viscous liquid

Existence of stationary solutions of the Navier–Stokes equations in the presence of a wall

“…We now rewrite (2), (9), (10), (12) and (13) as evolution equations with z playing the role of time. Namely, as is easily veri…ed, these equations are equivalent to…”

“…Interesting recent experimental work is described in [19,20]. Numerical studies can be found in [4,6,12,17].…”

An efficient front-tracking solver for thermocapillary migration simulations

“…The Front-tracking scheme [9][10][11][12], the Level-set scheme [13] and the Volume of fluid scheme (VOF) [14] are methods proved to be useful for moving-interface problem. The advantage of the Front-tracking scheme is the more precise determination of the interface position, which is normally 1/100∼1/1000 of the mesh size.…”

Fast and robust solvers for pressure-correction in bubbly flow problems

“…Computation of two-phase flows and, in particular, bubbly flows is a very active research topic in computational fluid dynamics (CFD), see, for instance, [7,12,37,[44][45][46][47] and, more recently, [17,23,35,38]. Understanding the dynamics and interaction of bubbles and droplets in a large variety of industrial processes is crucial for economically and ecologically optimized design.…”

“…The solution of the pressure-correction equation within such operator-splitting approaches has long been recognized as a computational bottleneck in fluid flow simulation, see, e.g., [6,17]. In the case of singlephase fluids, a common approach to overcoming this bottleneck is the use of multigrid solvers for this equation [43].…”