GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
The NURBS book
On the Cahn-Hilliard equation with degenerate mobility
SIAM Journal on Mathematical Analysis
Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Accurate Parametrization of Conics by NURBS
IEEE Computer Graphics and Applications
Computation of multiphase systems with phase field models
Journal of Computational Physics
A discontinuous Galerkin method for the Cahn-Hilliard equation
Journal of Computational Physics
On large time-stepping methods for the Cahn--Hilliard equation
Applied Numerical Mathematics
Diffuse interface model for incompressible two-phase flows with large density ratios
Journal of Computational Physics
A time-adaptive finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky equations
Journal of Computational Physics
A class of stable spectral methods for the Cahn-Hilliard equation
Journal of Computational Physics
Isogeometric Analysis: Toward Integration of CAD and FEA
Isogeometric Analysis: Toward Integration of CAD and FEA
Journal of Computational Physics
Hi-index | 31.45 |
We present a numerical study of the spinodal decomposition of a binary fluid undergoing shear flow using the advective Cahn-Hilliard equation, a stiff, nonlinear, parabolic equation characterized by the presence of fourth-order spatial derivatives. Our numerical solution procedure is based on isogeometric analysis, an approximation technique for which basis functions of high-order continuity are employed. These basis functions allow us to directly discretize the advective Cahn-Hilliard equation without resorting to a mixed formulation. We present steady state solutions for rectangular domains in two-dimensions and, for the first time, in three-dimensions. We also present steady state solutions for the two-dimensional Taylor-Couette cell. To enforce periodic boundary conditions in this curved domain, we derive and utilize a new periodic Bezier extraction operator. We present an extensive numerical study showing the effects of shear rate, surface tension, and the geometry of the domain on the phase evolution of the binary fluid. Theoretical and experimental results are compared with our simulations.