Qiaolin He

TL;DR: This article discusses the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall and uses a least-squares/conjugate gradient method.

TL;DR: In this paper, the Navier slip boundary condition has been used to remove the corner singularity induced by the no-slip boundary condition, which has been shown to increase the critical Reynolds number for Hopf bifurcation.

TL;DR: In this paper, the evolution of the periodic boundary value problem and the mixed boundary value problems for a compressible mixture of binary fluids modeled by the Navier-Stokes-Cahn-Hilliard system in one dimensional space are studied.

TL;DR: In this article, a least-squares/fictitious domain method for the solution of linear elliptic boundary value problems with Robin boundary conditions was proposed, where one solves a variant of the original problem on the full W, followed by a chosen correction over w. This method is of the virtual control type and relies on a least square formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space.

TL;DR: In this paper, the authors studied the linearized stability of shear flow satisfying Navier slip boundary conditions and showed that slip at the boundary increases the critical Reynolds number Rc for instability.