A numerical scheme for particle-laden thin film flow in two dimensions

Simulation of thin film flows with a moving mesh mixed finite element method

“…Although we are not able to prove similar properties for the adaptive mesh obtained using the moving mesh strategy with monitor smoothed by the 2D extension (27), we numerically show that the adaptive mesh has similar properties:…”

“…The effects of the moving framework for fourth-order equations have been studied by [11,27], their results show that the moving framework gives consistent solutions as the fixed framework.…”

Thin-liquid-film flow on three-dimensional topographically patterned rotating cylinders

“…Given a set of dimensionless parameters (table 2) and initial conditions, (2.18) is solved using an alternating-direction implicit (ADI) finite-difference scheme similar to that of Mata & Bertozzi (2011). The spatial domain is discretized using a uniform grid of points, where the grid spacing is defined as and the length of the cylinder is defined as .…”

“…The spatial domain is discretized using a uniform grid of points, where the grid spacing is defined as and the length of the cylinder is defined as . An initial time step of is set, and an adaptive time-stepping method similar to that of Mata & Bertozzi (2011) is used to determine the time step during simulations. Spatial derivatives are approximated using second-order centred finite differences, while the time-stepping is done using a semi-implicit scheme.…”

“…At each time step, an iterative procedure is applied to reduce computational time and to improve solution accuracy (Mata & Bertozzi 2011; Li & Kumar 2018). Periodic boundary conditions are applied in both the angular direction () and the axial direction ().…”