Singularities and similarities in interface flows
Trends and perspectives in applied mathematics
Positivity-Preserving Numerical Schemes for Lubrication-Type Equations
SIAM Journal on Numerical Analysis
Numerical Analysis of Coupled Systems of Nonlinear Parabolic Equations
SIAM Journal on Numerical Analysis
Computing three-dimensional thin film flows including contact lines
Journal of Computational Physics
ADI schemes for higher-order nonlinear diffusion equations
Applied Numerical Mathematics
A parallel hybrid banded system solver: the SPIKE algorithm
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
Journal of Computational Physics
A high-order ADI method for parabolic problems with variable coefficients
International Journal of Computer Mathematics
A tearing-based hybrid parallel banded linear system solver
Journal of Computational and Applied Mathematics
FDM for multi-dimensional nonlinear coupled system of parabolic and hyperbolic equations
Journal of Computational and Applied Mathematics
Hi-index | 31.45 |
The physics of particle-laden thin film flow is not fully understood, and recent experiments have raised questions with current theory. There is a need for fully two-dimensional simulations to compare with experimental data. To this end, a numerical scheme is presented for a lubrication model derived for particle-laden thin film flow in two dimensions with surface tension. The scheme relies on an ADI process to handle the higher-order terms, and an iterative procedure to improve the solution at each timestep. This is the first paper to simulate the two-dimensional particle-laden thin film lubrication model. Several aspects of the scheme are examined for a test problem, such as the timestep, runtime, and number of iterations. The results from the simulation are compared to experimental data. The simulation shows good qualitative agreement. It also suggests further lines of inquiry for the physical model.