We investigate the parameterization of deep neural networks that by design satisfy the
continuity equation, a fundamental conservation law. This is enabled by the observation that …

In this paper a conservative phase-field method based on the work of Sun and Beckermann
[Y. Sun, C. Beckermann, Sharp interface tracking using the phase-field equation, J. Comput …

We investigate the applicability of an incompressible diffuse interface model for two-phase
incompressible fluid flows with large viscosity and density contrasts. Diffuse-interface …

In this paper we construct two classes, based on stabilization and convex splitting, of
decoupled, unconditionally energy stable schemes for Cahn--Hilliard phase-field models of …

A lattice Boltzmann model (LBM) is proposed based on the phase-field theory to simulate
incompressible binary fluids with density and viscosity contrasts. Unlike many existing …

We present the latest developments of our High-Order Spectral Element Solver (Image 1),
an open source high-order discontinuous Galerkin framework, capable of solving a variety of …

Modeling and numerical approximation of two-phase incompressible flows with different
densities and viscosities are considered. A physically consistent phase-field model that …

In this paper, a phase-field-based multiple-relaxation-time lattice Boltzmann (LB) model is
proposed for incompressible multiphase flow systems. In this model, one distribution …

In this paper, we establish a binary fluid surfactant model by coupling two mass-conserved
Allen–Cahn equations and the Navier–Stokes equations and consider numerical …

A multiphase lattice Boltzmann flux solver (MLBFS) is proposed in this paper for
incompressible multiphase flows with low-and large-density-ratios. In the solver, the flow …