▪ Abstract We provide an overview of level set methods, introduced by Osher and Sethian,
for computing the solution to fluid-interface problems. These are computational techniques …

We consider multiphysics applications from algorithmic and architectural perspectives,
where “algorithmic” includes both mathematical analysis and computational complexity, and …

AMReX is a C++ software framework that supports the development of block-structured
adaptive mesh refinement (AMR) algorithms for solving systems of partial differential …

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 …

A method combining an adaptive quad/octree spatial discretisation, geometrical Volume-Of-
Fluid interface representation, balanced-force continuum-surface-force surface-tension …

A new N-body and hydrodynamical code, called RAMSES, is presented. It has been
designed to study structure formation in the universe with high spatial resolution. The code is …

We present a coupled level set/volume-of-fluid (CLSVOF) method for computing 3D and
axisymmetric incompressible two-phase flows. This method combines some of the …

In this paper, we review the recent development of phase-field models and their numerical
methods for multi-component fluid flows with interfacial phenomena. The models consist of a …

An adaptive mesh projection method for the time-dependent incompressible Euler equations
is presented. The domain is spatially discretised using quad/octrees and a multilevel …

Reacting flow simulations for combustion applications require extensive computing
capabilities. Leveraging the AMReX library, the Pele suite of combustion simulation tools …