Front tracking applied to Rayleigh Taylor instability
SIAM Journal on Scientific and Statistical Computing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
Projection method I: convergence and numerical boundary layers
SIAM Journal on Numerical Analysis
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics)
A phase-field method for interface-tracking simulation of two-phase flows
Mathematics and Computers in Simulation - Special issue: Discrete simulation of fluid dynamics in complex systems
Numerical Methods for Two-Dimensional Stem Cell Tissue Growth
Journal of Scientific Computing
Hi-index | 31.45 |
We present a new algorithm to numerically simulate two-dimensional viscous incompressible flows with moving interfaces. The motion is updated in time by using the backward difference formula through an iterative procedure. At each iteration, the pseudo-spectral technique is applied in the horizontal direction. The resulting semi-discretized equations constitute a boundary value problem in the vertical coordinate which is solved by decoupling growing and decaying solutions. Numerical tests justify that this method achieves fully second-order accuracy in both the temporal variable and vertical coordinate. As an application of this algorithm, we study the motion of Stokes waves in the presence of viscosity. Our numerical results are consistent with the recently published asymptotic solution for Stokes waves in slightly viscous fluids.