Related papers: Third-Order Geometric-Volume Conservation in Cahn-…
In this paper we present a conservative cell-centered Lagrangian finite volume scheme for the solution of the hyper-elasticity equations on unstructured multidimensional grids. The starting point of the new method is the Eucclhyd scheme,…
It is shown analytically that the energy-conserving implicit nonsymplectic scheme of Bacchini, Ripperda, Chen and Sironi provides a first-order accuracy to numerical solutions of a six-dimensional conservative Hamiltonian system. Because of…
The Cahn--Hilliard equations are a versatile model for describing the evolution of complex morphologies. In this paper we present a computational pipeline for the numerical solution of a ternary phase-field model for describing the…
We present an energy-preserving mechanic formulation for dynamic quasi-brittle fracture in an Eulerian-Lagrangian formulation, where a second-order phase-field equation controls the damage evolution. The numerical formulation adapts in…
The Cahn-Hilliard-Navier-Stokes (CHNS) system utilizes a diffusive phase-field for interface tracking of multi-phase fluid flows. Recently structure preserving methods for CHNS have moved into focus to construct numerical schemes that, for…
We present a novel data-driven approach for enhancing gradient reconstruction in unstructured finite volume methods for hyperbolic conservation laws, specifically for the 2D Euler equations. Our approach extends previous structured-grid…
We describe a charge-conserving scatter-gather algorithm for particle-in-cell simulations on unstructured grids. Charge conservation is obtained from first principles, i.e., without the need for any post-processing or correction steps. This…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
We establish metastability of the one-dimensional Cahn-Hilliard equation for initial data that is order-one in energy and order-one in $\dot{H}^{-1}$ away from a point on the so-called slow manifold with $N$ well-separated layers.…
We present a rigorous analysis of the transient evolution of nearly circular bilayer interfaces evolving under the thin interface limit, $\varepsilon\ll1$, of the mass preserving $L^2$-gradient flow of the strong scaling of the…
A high-order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the $Q_k$ finite element with mass lumping on rectangular grids, the second-order…
The Cahn-Hilliard equation has a wide range of applications in many areas of physics and chemistry. To describe the short-range interaction between the solution and the boundary, scientists have constructed dynamical boundary conditions by…
In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172--1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to…
Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…
In this paper, a third-order compact gas-kinetic scheme is firstly proposed for three-dimensional computation for the compressible Euler and Navier-Stokes solutions. The scheme achieves its compactness due to the time-dependent gas…
Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…
Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures…
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…
We present an interface and geometry preserving (IGP) method for the modeling of fully Eulerian fluid-structure interaction via phase-field formulation. While the hyperbolic tangent interface profile is preserved by the time-dependent…
In this note, we study the optimal control of a nonisothermal phase field system of Cahn-Hilliard type that constitutes an extension of the classical Caginalp model for nonisothermal phase transitions with a conserved order parameter. It…