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Phase fields models offer a systematic physical approach for investigating complex multiphase systems behaviors such as near-critical interfacial phenomena, phase separation under shear, and microstructure evolution during solidification. However , because interfaces are replaced by thin transition regions (diffuse interfaces), phase field simulations… (More)

We introduce a method for solving the variable coefficient Poisson equation on non-graded Cartesian grids that yields second order accuracy for the solutions and their gradients. We employ quadtree (in 2D) and octree (in 3D) data structures as an efficient means to represent the Cartesian grid, allowing for constraint-free grid generation. The schemes take… (More)

We present a nonstiff, fully adaptive mesh refinement-based method for the Cahn-Hilliard equation. The method is based on a semi-implicit splitting, in which linear leading order terms are extracted and discretized implicitly, combined with a robust adaptive spatial discretization. The fully discretized equation is written as a system which is efficiently… (More)

We present an efficient numerical methodology for the 3D computation of incom-pressible multi-phase flows described by conservative phase field models. We focus here on the case of density matched fluids with different viscosity (Model H). The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time… (More)

We propose efficient pseudospectral numerical schemes for solving the self-consistent, mean-field equations for inhomogeneous polymers. In particular, we introduce a robust class of semi-implicit methods that employ asymptotic small scale information about the nonlocal density operators. The relaxation schemes are further embedded in a multilevel strategy… (More)

- Jack Xin, M Avellaneda, G Bal, A L Bertozzi, L Borcea, R Caflisch +42 others
- 2016

MMS features research articles that focus on the fundamental modeling and computational principles underlying various multiscale methods. Multiscale modeling is highly interdisciplinary, with developments occurring independently across fields. Research papers and survey articles that augment the fundamental ways we model and predict multiscale phenomena are… (More)

The Immersed Boundary Method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit dis-cretizations. This excessive stability constraint can… (More)

We propose a fast and non-stiff approach for the solutions of the Immersed Boundary Method, for Newtonian, incompressible flows in two or three dimensions. The proposed methodology is built on a robust semi-implicit dis-cretization introduced by Peskin in the late 70's which is solved efficiently through the novel use of a fast, treecode strategy to compute… (More)

When binary liquid mixtures are cooled rapidly from a homogeneous phase into a two-phase system, domains of the two equilibrium phases form and grow (coarsen) with time. In the absence of an external forcing due to gravity or an imposed shear flow, a dynamic scaling regime emerges in which the domain morphology is statistically self-similar at different… (More)

Boundary integral methods to simulate interfacial flows are very sensitive to numerical instabilities. In addition, surface tension introduces nonlinear terms with high order spatial derivatives into the interface dynamics. This makes the spatial discretization even more difficult and, at the same time, imposes a severe time step constraint for stable… (More)